Random problems from Sections 5.1, 5.3, 5.4, 5.6, and 5.7. Choose a section, get a problem, then reveal the answer.
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Section 5.1 · Problem 47
Calculate the limit of the Riemann sum for the given function and interval. Verify the result using geometry.
\( f(x)=9x,\ 0\le x\le 2 \)
Answer: \( 18 \)
Section 5.1 · Problem 48
Calculate the limit of the Riemann sum for the given function and interval. Verify the result using geometry.
\( f(x)=3x+6,\ 1\le x\le 4 \)
Answer: \( \frac{81}{2} \)
Section 5.1 · Problem 49
Calculate the limit of the Riemann sum for the given function and interval. Verify the result using geometry.
\( f(x)=\tfrac{1}{2}x+2,\ 0\le x\le 4 \)
Answer: \( 12 \)
Section 5.1 · Problem 50
Calculate the limit of the Riemann sum for the given function and interval. Verify the result using geometry.
\( f(x)=4x-2,\ 1\le x\le 3 \)
Answer: \( 12 \)
Section 5.1 · Problem 51
Calculate the limit of the Riemann sum for the given function and interval. Verify the result using geometry.
\( f(x)=x,\ 0\le x\le 2 \)
Answer: \( 2 \)
Section 5.1 · Problem 52
Calculate the limit of the Riemann sum for the given function and interval. Verify the result using geometry.
\( f(x)=12-4x,\ 2\le x\le 6 \)
Answer: \( -16 \)
Section 5.1 · Problem 55
Find a formula for \(R_N\) and compute the area under the graph as a limit.
\( f(x)=x^2,\ 1\le x\le 3 \)
Answer: \( \dfrac{26}{3} \)
Section 5.1 · Problem 56
Find a formula for \(R_N\) and compute the area under the graph as a limit.
\( f(x)=x^2,\ -1\le x\le 5 \)
Answer: \( 42 \)
Section 5.1 · Problem 57
Find a formula for \(R_N\) and compute the area under the graph as a limit.
\( f(x)=6x^2-4,\ 2\le x\le 5 \)
Answer: \( 222 \)
Section 5.1 · Problem 58
Find a formula for \(R_N\) and compute the area under the graph as a limit.
\( f(x)=x^2+7x,\ 6\le x\le 11 \)
Answer: \( \dfrac{4015}{6} \)
Section 5.1 · Problem 59
Find a formula for \(R_N\) and compute the area under the graph as a limit.
\( f(x)=x^3-x,\ 0\le x\le 2 \)
Answer: \( 2 \)
Section 5.3 · Problem 1
Find the general antiderivative of \(f\) and verify your result by differentiating.
\( f(x)=18x^2 \)
Answer: \( 6x^3 + C \)
Section 5.3 · Problem 2
Find the general antiderivative of \(f\) and verify your result by differentiating.
\( f(x)=x^{-3/5} \)
Answer: \( \dfrac{5}{2}x^{2/5} + C \)
Section 5.3 · Problem 3
Find the general antiderivative of \(f\) and verify your result by differentiating.
\( f(x)=2x^4-24x^2 \)
Answer: \( \dfrac{2}{5}x^5 - 8x^3 + C \)
Section 5.3 · Problem 4
Find the general antiderivative of \(f\) and verify your result by differentiating.
\( f(x)=9x+15x^{-2} \)
Answer: \( \dfrac{9}{2}x^2 - \dfrac{15}{x} + C \)
Section 5.3 · Problem 5
Find the general antiderivative of \(f\) and verify your result by differentiating.
\( f(x)=2\cos x - 9\sin x \)
Answer: \( 2\sin x + 9\cos x + C \)
Section 5.3 · Problem 6
Find the general antiderivative of \(f\) and verify your result by differentiating.
\( f(x)=4x^7 - 3\cos x \)
Answer: \( \dfrac{1}{2}x^8 - 3\sin x + C \)
Section 5.3 · Problem 7
Find the general antiderivative of \(f\) and verify your result by differentiating.
\( f(x)=\sin(2x)+12\cos(3x) \)
Answer: \( -\tfrac{1}{2}\cos(2x) + 4\sin(3x) + C \)
Section 5.3 · Problem 8
Find the general antiderivative of \(f\) and verify your result by differentiating.
\( f(x)=\sin(4-9x) \)
Answer: \( \dfrac{1}{9}\cos(9x-4) + C \)
Section 5.3 · Problem 10
Evaluate the indefinite integral.
\( \displaystyle \int (9x+2)\,dx \)
Answer: \( \dfrac{9}{2}x^2 + 2x + C \)
Section 5.3 · Problem 11
Evaluate the indefinite integral.
\( \displaystyle \int (4-18x)\,dx \)
Answer: \( 4x - 9x^2 + C \)
Section 5.3 · Problem 12
Evaluate the indefinite integral.
\( \displaystyle \int x^{-3}\,dx \)
Answer: \( -\dfrac{1}{2x^2} + C \)
Section 5.3 · Problem 13
Evaluate the indefinite integral.
\( \displaystyle \int t^{-6/11}\,dt \)
Answer: \( \dfrac{11}{5}t^{5/11} + C \)
Section 5.3 · Problem 14
Evaluate the indefinite integral.
\( \displaystyle \int (5t^3 - t^{-3})\,dt \)
Answer: \( \dfrac{5}{4}t^4 + \dfrac{1}{2}t^{-2} + C \)
Section 5.3 · Problem 15
Evaluate the indefinite integral.
\( \displaystyle \int (18t^5 - 10t^4 - 28t)\,dt \)
Answer: \( 3t^6 - 2t^5 - 14t^2 + C \)
Section 5.3 · Problem 16
Evaluate the indefinite integral.
\( \displaystyle \int 14s^{9/5}\,ds \)
Answer: \( 5s^{14/5} + C \)
Section 5.3 · Problem 17
Evaluate the indefinite integral.
\(
\displaystyle \int (z^{-4/5} - z^{2/3} + z^{5/4})\,dz
\)
Answer: \( 5z^{1/5} - \dfrac{3}{5}z^{5/3} + \dfrac{4}{9}z^{9/4} + C \)
Section 5.3 · Problem 18
Evaluate the indefinite integral.
\( \displaystyle \int \frac{3}{2}\,dx \)
Answer: \( \dfrac{3}{2}x + C \)
Section 5.3 · Problem 19
Evaluate the indefinite integral.
\( \displaystyle \int x^{-1/3}\,dx \)
Answer: \( \dfrac{3}{2}x^{2/3} + C \)
Section 5.3 · Problem 20
Evaluate the indefinite integral.
\( \displaystyle \int x^{-4/3}\,dx \)
Answer: \( -\dfrac{3}{x^{1/3}} + C \)
Section 5.3 · Problem 21
Evaluate the indefinite integral.
\( \displaystyle \int 36t^{-3}\,dt \)
Answer: \( -\dfrac{18}{t^2} + C \)
Section 5.3 · Problem 22
Evaluate the indefinite integral.
\( \displaystyle \int x(x^2-4)\,dx \)
Answer: \( \dfrac{1}{4}x^4 - 2x^2 + C \)
Section 5.3 · Problem 23
Evaluate the indefinite integral.
\(
\displaystyle \int (t^{1/2}+1)(t+1)\,dt
\)
Answer: \( \dfrac{2}{5}t^{5/2} + \dfrac{2}{3}t^{3/2} + \dfrac{1}{2}t^2 + t + C \)
Section 5.3 · Problem 24
Evaluate the indefinite integral.
\(
\displaystyle \int \frac{12-z}{\sqrt{z}}\,dz
\)
Answer: \( 24\sqrt{z} - \dfrac{2}{3}z^{3/2} + C \)
Section 5.3 · Problem 25
Evaluate the indefinite integral.
\(
\displaystyle \int \frac{x^3-4}{x^2}\,dx
\)
Answer: \( \dfrac{1}{2}x^2 + \dfrac{4}{x} + C \)
Section 5.3 · Problem 27
Evaluate the indefinite integral.
\( \displaystyle \int 12\sec x \tan x\,dx \)
Answer: \( 12\sec x + C \)
Section 5.3 · Problem 28
Evaluate the indefinite integral.
\(
\displaystyle \int (\theta + \sec^2\theta)\,d\theta
\)
Answer: \( \dfrac{1}{2}\theta^2 + \tan\theta + C \)
Section 5.3 · Problem 29
Evaluate the indefinite integral.
\( \displaystyle \int \csc t \cot t\,dt \)
Answer: \( -\csc t + C \)
Section 5.3 · Problem 30
Evaluate the indefinite integral.
\(
\displaystyle \int (t - \sin t)\,dt
\)
Answer: \( \dfrac{1}{2}t^2 + \cos t + C \)
Section 5.3 · Problem 31
Evaluate the indefinite integral.
\(
\displaystyle \int (x^2 - \sec^2 x)\,dx
\)
Answer: \( \dfrac{1}{3}x^3 - \tan x + C \)
Section 5.3 · Problem 32
Evaluate the indefinite integral.
\( \displaystyle \int \tan\theta \cos\theta\,d\theta \)
Answer: \( -\cos\theta + C \)
Section 5.4 · Problem 5
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{3}^{6} x\,dx \)
Answer: \( \dfrac{27}{2} \)
Section 5.4 · Problem 6
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{0}^{9} 2\,dx \)
Answer: \( 18 \)
Section 5.4 · Problem 7
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{0}^{1} (4x - 9x^2)\,dx \)
Answer: \( -1 \)
Section 5.4 · Problem 8
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{-3}^{2} u^2\,du \)
Answer: \( \dfrac{35}{3} \)
Section 5.4 · Problem 9
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\(
\displaystyle \int_{0}^{2} (12x^5 + 3x^2 - 4x)\,dx
\)
Answer: \( 128 \)
Section 5.4 · Problem 10
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\(
\displaystyle \int_{-2}^{2} (10x^9 + 3x^5)\,dx
\)
Answer: \( 0 \)
Section 5.4 · Problem 11
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\(
\displaystyle \int_{3}^{0} (2t^3 - 6t^2)\,dt
\)
Answer: \( \dfrac{27}{2} \)
Section 5.4 · Problem 12
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\(
\displaystyle \int_{-1}^{1} (5u^4 + u^2 - u)\,du
\)
Answer: \( \dfrac{8}{3} \)
Section 5.4 · Problem 13
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{0}^{4} \sqrt{y}\,dy \)
Answer: \( \dfrac{16}{3} \)
Section 5.4 · Problem 14
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{1}^{8} x^{4/3}\,dx \)
Answer: \( \dfrac{381}{7} \)
Section 5.4 · Problem 15
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{1/16}^{1} t^{1/4}\,dt \)
Answer: \( \dfrac{31}{40} \)
Section 5.4 · Problem 16
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{4}^{1} t^{5/2}\,dt \)
Answer: \( -\dfrac{254}{7} \)
Section 5.4 · Problem 17
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{1}^{3} t^{-2}\,dt \)
Answer: \( \dfrac{2}{3} \)
Section 5.4 · Problem 18
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{1}^{4} x^{-4}\,dx \)
Answer: \( \dfrac{21}{64} \)
Section 5.4 · Problem 19
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\(
\displaystyle \int_{1/2}^{1} 8x^{-3}\,dx
\)
Answer: \( 12 \)
Section 5.4 · Problem 20
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{-2}^{-1} x^{-3}\,dx \)
Answer: \( -\dfrac{3}{8} \)
Section 5.4 · Problem 21
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\(
\displaystyle \int_{1}^{2} (x^2 - x^{-2})\,dx
\)
Answer: \( \dfrac{11}{6} \)
Section 5.4 · Problem 22
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{1}^{9} t^{-1/2}\,dt \)
Answer: \( 4 \)
Section 5.4 · Problem 23
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\(
\displaystyle \int_{1}^{27} \frac{t+1}{\sqrt{t}}\,dt
\)
Answer: \( -\dfrac{8}{3} + 60\sqrt{3} \)
Section 5.4 · Problem 24
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\(
\displaystyle \int_{8/27}^{1} \frac{10t^{4/3} - 8t^{1/3}}{t^2}\,dt
\)
Answer: \( -5 \)
Section 5.4 · Problem 25
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\(
\displaystyle \int_{-\pi/4}^{\pi} \sin\theta\,d\theta
\)
Answer: \( 1 + \dfrac{\sqrt{2}}{2} \)
Section 5.4 · Problem 26
Evaluate using the Fundamental Theorem of Calculus, Part I (FTC I).
\( \displaystyle \int_{0}^{13\pi} \sin x\,dx \)
Answer: \( 2 \)
Section 5.6 · Problem 9
A particle moves in a straight line with the given velocity \(v(t)\). Find the displacement and total distance traveled over the time interval.
\( v(t)=12-4t,\ 0\le t\le 5 \)
Answer: Displacement \(=-10\), Distance \(=15\)
Section 5.6 · Problem 10
A particle moves in a straight line with the given velocity \(v(t)\). Find the displacement and total distance traveled over the time interval.
\( v(t)=36-24t+3t^2,\ 0\le t\le 10 \)
Answer: Displacement \(=60\), Distance \(=96\)
Section 5.7 · Problem 27
Evaluate the indefinite integral.
\( \displaystyle \int (4x+5)^9\,dx \)
Answer: \( \dfrac{(4x+5)^{10}}{40} + C \)
Section 5.7 · Problem 28
Evaluate the indefinite integral.
\( \displaystyle \int \frac{dx}{(x-9)^5} \)
Answer: \( -\dfrac{1}{4(x-9)^4} + C \)
Section 5.7 · Problem 29
Evaluate the indefinite integral.
\( \displaystyle \int \frac{dt}{\sqrt{t+12}} \)
Answer: \( 2\sqrt{t+12} + C \)
Section 5.7 · Problem 30
Evaluate the indefinite integral.
\( \displaystyle \int (9t+2)^{2/3}\,dt \)
Answer: \( \dfrac{1}{15}(9t+2)^{5/3} + C \)
Section 5.7 · Problem 31
Evaluate the indefinite integral.
\( \displaystyle \int \frac{x+1}{(x^2+2x)^3}\,dx \)
Answer: \( -\dfrac{1}{4(x^2+2x)^2} + C \)
Section 5.7 · Problem 32
Evaluate the indefinite integral.
\( \displaystyle \int (x+1)(x^2+2x)^{3/4}\,dx \)
Answer: \( \dfrac{2}{7}(x^2+2x)^{7/4} + C \)
Section 5.7 · Problem 33
Evaluate the indefinite integral.
\( \displaystyle \int \frac{x}{\sqrt{x^2+9}}\,dx \)
Answer: \( \sqrt{x^2+9} + C \)
Section 5.7 · Problem 34
Evaluate the indefinite integral.
\( \displaystyle \int \frac{2x^2+x}{(4x^3+3x^2)^2}\,dx \)
Answer: \( -\dfrac{1}{6(4x^3+3x^2)} + C \)
Section 5.7 · Problem 35
Evaluate the indefinite integral.
\( \displaystyle \int (2x^3-7)^2\,dx \)
Answer: \( \dfrac{4}{7}x^7 - 7x^4 + 49x + C \)
Section 5.7 · Problem 36
Evaluate the indefinite integral.
\( \displaystyle \int (4-x^3)^2\,dx \)
Answer: \( \dfrac{1}{7}x^7 - 2x^4 + 16x + C \)
Section 5.7 · Problem 37
Evaluate the indefinite integral.
\( \displaystyle \int x^2(2x^3-7)^3\,dx \)
Answer: \( \dfrac{(2x^3-7)^4}{24} + C \)
Section 5.7 · Problem 38
Evaluate the indefinite integral.
\( \displaystyle \int 6x^2(4-x^3)^4\,dx \)
Answer: \( -\dfrac{2}{5}(4-x^3)^5 + C \)
Section 5.7 · Problem 39
Evaluate the indefinite integral.
\( \displaystyle \int (3x+8)^{11}\,dx \)
Answer: \( \dfrac{(3x+8)^{12}}{36} + C \)
Section 5.7 · Problem 40
Evaluate the indefinite integral.
\( \displaystyle \int x(3x+8)^{11}\,dx \)
Answer: \( \dfrac{(3x+8)^{13}}{117} - \dfrac{2(3x+8)^{12}}{27} + C \)
Section 5.7 · Problem 41
Evaluate the indefinite integral.
\( \displaystyle \int x^2\sqrt{x^3+1}\,dx \)
Answer: \( \dfrac{2}{9}(x^3+1)^{3/2} + C \)
Section 5.7 · Problem 42
Evaluate the indefinite integral.
\( \displaystyle \int x^5\sqrt{x^3+1}\,dx \)
Answer: \( \dfrac{2}{15}(x^3+1)^{5/2} - \dfrac{2}{9}(x^3+1)^{3/2} + C \)
Section 5.7 · Problem 43
Evaluate the indefinite integral.
\( \displaystyle \int \frac{dx}{(x+5)^3} \)
Answer: \( -\dfrac{1}{2(x+5)^2} + C \)
Section 5.7 · Problem 44
Evaluate the indefinite integral.
\( \displaystyle \int \frac{x^2}{(x+5)^3}\,dx \)
Answer: \( \ln|x+5| + \dfrac{10}{x+5} - \dfrac{25}{2(x+5)^2} + C \)
Section 5.7 · Problem 45
Evaluate the indefinite integral.
\( \displaystyle \int z^2(z^3+1)^{12}\,dz \)
Answer: \( \dfrac{(z^3+1)^{13}}{39} + C \)
Section 5.7 · Problem 46
Evaluate the indefinite integral.
\( \displaystyle \int (z^5+4z^2)(z^3+1)^{12}\,dz \)
Answer: \( \dfrac{(z^3+1)^{14}}{42} + \dfrac{(z^3+1)^{13}}{13} + C \)
Section 5.7 · Problem 47
Evaluate the indefinite integral.
\( \displaystyle \int (x+2)(x+1)^{1/4}\,dx \)
Answer: \( \dfrac{4}{9}(x+1)^{9/4} + \dfrac{4}{5}(x+1)^{5/4} + C \)
Section 5.7 · Problem 48
Evaluate the indefinite integral.
\( \displaystyle \int x^3(x^2-1)^{3/2}\,dx \)
Answer: \( \dfrac{(x^2-1)^{7/2}}{7} + \dfrac{(x^2-1)^{5/2}}{5} + C \)
Section 5.7 · Problem 49
Evaluate the indefinite integral.
\( \displaystyle \int \sin(8-3\theta)\,d\theta \)
Answer: \( \dfrac{1}{3}\cos(8-3\theta) + C \)
Section 5.7 · Problem 50
Evaluate the indefinite integral.
\( \displaystyle \int \theta\sin(\theta^2)\,d\theta \)
Answer: \( -\dfrac{1}{2}\cos(\theta^2) + C \)
Section 5.7 · Problem 51
Evaluate the indefinite integral.
\( \displaystyle \int \frac{\cos\sqrt{t}}{\sqrt{t}}\,dt \)
Answer: \( 2\sin\sqrt{t} + C \)
Section 5.7 · Problem 52
Evaluate the indefinite integral.
\( \displaystyle \int x^2\sin(x^3+1)\,dx \)
Answer: \( -\dfrac{1}{3}\cos(x^3+1) + C \)
Section 5.7 · Problem 53
Evaluate the indefinite integral.
\( \displaystyle \int \frac{\sin x\cos x}{\sqrt{\sin x+1}}\,dx \)
Answer: \( \dfrac{2}{3}(\sin x+1)^{3/2} - 2\sqrt{\sin x+1} + C \)
Section 5.7 · Problem 54
Evaluate the indefinite integral.
\( \displaystyle \int \sin^8\theta\cos\theta\,d\theta \)
Answer: \( \dfrac{\sin^9\theta}{9} + C \)
Section 5.7 · Problem 55
Evaluate the indefinite integral.
\( \displaystyle \int \sec^2x(12\tan^3x-6\tan^2x)\,dx \)
Answer: \( 3\tan^4x - 2\tan^3x + C \)
Section 5.7 · Problem 56
Evaluate the indefinite integral.
\( \displaystyle \int x^{-1/5}\sec(x^{4/5})\tan(x^{4/5})\,dx \)
Answer: \( \dfrac{5}{4}\sec(x^{4/5}) + C \)
Section 5.7 · Problem 57
Evaluate the indefinite integral.
\( \displaystyle \int \sec^2(4x+9)\,dx \)
Answer: \( \dfrac{1}{4}\tan(4x+9) + C \)
Section 5.7 · Problem 58
Evaluate the indefinite integral.
\( \displaystyle \int \sec^2x\tan^4x\,dx \)
Answer: \( \dfrac{1}{5}\tan^5x + C \)
Section 5.7 · Problem 59
Evaluate the indefinite integral.
\( \displaystyle \int \frac{\sec^2\sqrt{x}}{\sqrt{x}}\,dx \)
Answer: \( 2\tan\sqrt{x} + C \)
Section 5.7 · Problem 60
Evaluate the indefinite integral.
\( \displaystyle \int \frac{\cos 2x}{(1+\sin 2x)^2}\,dx \)
Answer: \( -\dfrac{1}{2(1+\sin 2x)} + C \)
Section 5.7 · Problem 61
Evaluate the indefinite integral.
\( \displaystyle \int \sin 4x\sqrt{\cos 4x+1}\,dx \)
Answer: \( -\dfrac{1}{6}(\cos 4x+1)^{3/2} + C \)
Section 5.7 · Problem 62
Evaluate the indefinite integral.
\( \displaystyle \int \cos x(3\sin x-1)\,dx \)
Answer: \( \dfrac{(3\sin x-1)^2}{6} + C \)
Section 5.7 · Problem 63
Evaluate the indefinite integral.
\( \displaystyle \int \sec\theta\tan\theta(\sec\theta-1)\,d\theta \)
Answer: \( \dfrac{1}{2}\sec^2\theta - \sec\theta + C \)
Section 5.7 · Problem 64
Evaluate the indefinite integral.
\( \displaystyle \int (\tan t + \sin t)\cos t\,dt \)
Answer: \( -\cos t - \dfrac{1}{2}\cos^2 t + C \)
Section 5.7 · Problem 73
Use the Change of Variables Formula to evaluate the definite integral.
\( \displaystyle \int_{0}^{2} \frac{1}{\sqrt{2x+5}}\,dx \)
Answer: \( 3 - \sqrt{5} \)
Section 5.7 · Problem 74
Use the Change of Variables Formula to evaluate the definite integral.
\( \displaystyle \int_{1}^{6} \sqrt{x+3}\,dx \)
Answer: \( \dfrac{38}{3} \)
Section 5.7 · Problem 75
Use the Change of Variables Formula to evaluate the definite integral.
\( \displaystyle \int_{0}^{1} \frac{x}{(x^2+1)^3}\,dx \)
Answer: \( \dfrac{3}{16} \)
Section 5.7 · Problem 76
Use the Change of Variables Formula to evaluate the definite integral.
\( \displaystyle \int_{-1}^{2} \sqrt{5x+6}\,dx \)
Answer: \( \dfrac{42}{5} \)
Section 5.7 · Problem 77
Use the Change of Variables Formula to evaluate the definite integral.
\( \displaystyle \int_{0}^{4} x\sqrt{x^2+9}\,dx \)
Answer: \( \dfrac{98}{3} \)