Calculus homework
dzaiki1. Find the area of the region enclosed by the curve y = x cos x and the x-axis for π ≤ x ≤ π.
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7π |
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8π |
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7 |
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9π |
4 points
QUESTION 2
1. Evaluate the integral.
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- y2 cos 7y + y sin 7y + cos 7y + C |
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y2 cos 7y - y sin 7y - cos 7y + C |
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- y2 cos 7y + y sin 7y + cos 7y + C |
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- y2 sin 7y + y cos 7y + sin 7y + C |
4 points
QUESTION 3
1. Evaluate the integral by using a substitution prior to integration by parts.
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x 2 + 2x - 2x + C |
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x 2 - x + x + C |
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x 2 - 2x + C |
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x 2 - 2x + 2x + C |
4 points
QUESTION 4
1. Evaluate the integral.
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2.68 |
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0.68 |
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6.68 |
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4.6 |
4 points
QUESTION 5
1. Evaluate the integral.
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Diverges |
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1 |
4 points
QUESTION 6
1. Evaluate the integral by using a substitution prior to integration by parts.
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ln (5x + 5x2) - 2x + C |
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xln (5x + 5x2) + C |
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xln (5x + 5x2) + ln (x +1) - 2x + C |
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ln (5x + 5x2) + ln (x +1) + C |
4 points
QUESTION 7
1. Evaluate the integral.
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ln 6x - + 2x + C |
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ln 6x - + x + C |
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ln 6x - + x + C |
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ln 6x - x2 + x + C |
4 points
QUESTION 8
1. Evaluate the integral. (Give your answer in exact form.)
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- |
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- |
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- |
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4 points
QUESTION 9
1. Evaluate the integral.
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ln 25x - + x + C |
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ln 25x - + x + C |
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ln 25x - x2 + x + C |
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ln 25x - + 2x + C |
4 points
QUESTION 10
1. Evaluate the integral.
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[7 sin 7x + 5 cos 7x] + C |
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[7 sin 7x - 5 cos 7x] + C |
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[ sin 7x + cos 7x] + C |
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[7 e5x sin 7x + 5 cos 7x] + C |
4 points
QUESTION 11
1. Evaluate the integral.
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- y4 e-4y + C |
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e-4y + C |
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- e-4y + C |
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-e-4y + C |
4 points
QUESTION 12
1. Evaluate the integral.
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[8 e3x sin 8x + 3 cos 8x] + C |
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[ sin 8x + cos 8x] + C |
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[8 sin 8x - 3 cos 8x] + C |
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[8 sin 8x + 3 cos 8x] + C |
4 points
QUESTION 13
1. Evaluate the integral.
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6.70 |
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12.64 |
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53.6 |
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74.6 |
4 points
QUESTION 14
1. Evaluate the integral.
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y2 cos 9y - y sin 9y - cos 9y + C |
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- y2 cos 9y + y sin 9y + cos 9y + C |
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- y2 sin 9y + y cos 9y + sin 9y + C |
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- y2 cos 9y + y sin 9y + cos 9y + C |
4 points
QUESTION 15
1. Evaluate the integral by using a substitution prior to integration by parts. dx
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- x(8 - x)3/2 + 8 - x)5/2 + C |
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x(8 - x)3/2 + (8 - x)5/2 + C |
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- x(8 - x)3/2 - (8 - x)5/2 + C |
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- x(8 - x)3/2 - (8 - x)5/2 + C |
4 points
QUESTION 16
1. Solve the problem. Find the area of the region enclosed by the curve y = x sin x and the x-axis for 7π ≤ x ≤ 8π.
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14π |
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0 |
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15π |
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14 |
4 points
QUESTION 17
1. Evaluate the integral.
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x3 sin 8x + x2 cos 8x - x sin 8x - cos 8x + C |
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x3 sin 8x + x2 cos 8x - x sin 8x - cos 8x + C |
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x3 cos 8x + x2 sin 8x - x cos 8x - sin 8x + C |
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x3 sin 8x - x2 cos 8x + x sin 8x + cos 8x + C |
4 points
QUESTION 18
1. Evaluate the integral.
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- x e-3x - e-3x + C |
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-21x e-3x - 75 e-3x + C |
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- x e-3x - e-3x + C |
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x e-3x + e-3x + C |
4 points
QUESTION 19
1. Evaluate the integral.
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x3 sin 9x + x2 cos 9x - x sin 9x - cos 9x + C |
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x3 sin 9x + x2 cos 9x - x sin 9x - cos 9x + C |
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x3 sin 9x - x2 cos 9x + x sin 9x + cos 9x + C |
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x3 cos 9x + x2 sin 9x - x cos 9x - sin 9x + C |
4 points
QUESTION 20
1. Evaluate the integral.
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ex[x2 - 8x + 8] + C |
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ex[x2 - 8x - 8] + C |
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x3ex - 3x2ex + C |
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ex[x2 - 6x + 6] + C |
4 points
QUESTION 21
1. Evaluate the integral. ln 3x dx
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17.53 |
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22.78 |
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16.78 |
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-6.80 |
4 points
QUESTION 22
1. Evaluate the integral by using a substitution prior to integration by parts.
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x[cos (ln x) + sin (ln x)] + C |
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[cos (ln x) + sin (ln x)] + C |
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[cos (ln x) - sin (ln x)] + C |
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x cos (ln x) + sin (ln x)+ C |
4 points
QUESTION 23
1. Evaluate the integral. ln 3x dx
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391.88 |
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384.07 |
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462.20 |
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-153.54 |
4 points
QUESTION 24
1. Evaluate the integral.
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x2e2x - xe2x + e2x + C |
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x2e2x - xe2x + e2x + C |
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x2e2x - e2x + C |
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x2e2x - xe2x + e2x + C |
4 points
QUESTION 25
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4π |
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π |
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2π |
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8π |