MAT 302 Assignment Problem 8.2

MAT 302 Assignment Problem 8.2 | Borough of Manhattan Community College

8.2 Integration by parts

Question 1

(1 point)

Solve ∫(11x+7)exdx∫(11x+7)exdx using Integration by Parts.

Use u=11x+7u=11x+7 and dv=exdxdv=exdx.

Question 2

 point) Use integration by parts to find the following:

∫(t+7)e2t+3dt

Question 3

(1 point) Use integration by parts to evaluate the integral.

Question 4

(1 point) Evaluate the indefinite integral.

∫lnxx6dx

Question 5

(1 point) Evaluate the integral.

∫3xsin(5x)dx∫3xsin⁡(5x)dx

Note: Use an upper-case "C" for the constant of integration.

Question 6

(1 point) Find the integral

Question 7

 (1 point) Find the integral.

∫e2xsin(7x)dx

Question 8

(1 point)

Evaluate the integral

∫e−1tcos(−2t)dt

Question 9

(1 point) Use integration by parts to evaluate the indefinite integral when x>0x>0

∫ln(x13)dx.

Question 10

(1 point) Evaluate the indefinite integral.

Question 11

(1 point) Evaluate the definite integral.

∫61t√ln(t)dt

Question 12

(1 point) Use integration by parts to evaluate the definite integral

∫70te−tdt.

Question 13

Evaluate the integral

∫108ye2ydy

Question 14

(1 point) Evaluate the integral

∫0.50.3cosx⋅ln(3sinx)dx.

Question 15

(1 point) If g(1)=2,g(1)=2, g(5)=6,g(5)=6, and ∫51g(x)dx=−6,∫15g(x)dx=−6, evaluate the integral ∫51xg′(x)dx.

Question 16

(1 point)

(a) Use the reduction formula

∫cosn(x)dx=1ncosn−1(x)sin(x)+n−1n∫cosn−2(x)dx∫cosn⁡(x)dx=1ncosn−1⁡(x)sin⁡(x)+n−1n∫cosn−2⁡(x)dx

to evaluate the integral

∫cos2(x)dx.

Question 17

(1 point)

Use the reduction formula

∫xnexdx=xnex−n∫xn−1exdx∫xnexdx=xnex−n∫xn−1exdx

to evaluate the integral

∫x4exdx.