Question

In: Math

(15) Evaluate each of the following integrals. (a) Z cos(x) ln(sin(x)) dx (b) Z x arcsin(x...

(15) Evaluate each of the following integrals. (a) Z cos(x) ln(sin(x)) dx (b) Z x arcsin(x 2 ) dx (c) Z 1 0 ln(1 + x 2 ) dx (d) Z 1/4 0 arcsin(2x) dx

(16) Use the table of integrals to evaluate the integrals, if needed. You may need to transform the integrand first.

(a) Z cos(4t) cos(5t)dt

(b) Z 1 cos3 (x) dx

(c) Z 1 x 2 + 6x + 9 dx

(d) Z 1 50 − 2y 2 dy

(e) Z x 3 cos(x 2 )dx (

f) Z x sin(3x 2 ) dx (g) Z dx √ 16x 2 + 36 (h) Z dx √ 81 − 25x 2

(17) Given the region bounded by the curves x + y = 3, 2x + y = 6, and x = 0. Find the volume of the solid generated by revolving this region about the y-axis.

(18) Given the region bounded by the curves x = |y| and x = 2 − y 2 . (a) Find the volume generated by revolving the region about the y-axis.

Solutions

Expert Solution

Solution : ( 15 )

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Solution : ( 16 )

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