AP Calculus BC
32 Integration by Parts
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Homework
Find the indefinite integral.
(1)
x e
4x
dx
(2)  t ln  t  1 dt
(3)

 ln x 2 dx
x
x e2 x
(4)

(5)
x
 2 x  1
2
dx
x  5dx
Willems – Unit 6: Integration Techniques, L’Hopital’s Rule & Improper Integrals
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(6)
 x cos xdx
(7)
 arctan xdx
(8) Solve the differential equation.
dy
 ln x
dx
Evaluate the definite integral.
3
(9)
x
x
2
e dx
0

4
(10)
 x cos  2 x  dx
0
Willems – Unit 6: Integration Techniques, L’Hopital’s Rule & Improper Integrals
5
1
2
(11)
 arccos xdx
0
Use the tabular method to find the integral.
(12)
x
2
e2x dx
(13)
x
3
sin xdx
Find the area of the region bounded by the graphs of the equations.
(14)
y  2 x e x , y  0, x  3
(15) y  ln x, y  0, x  e
Willems – Unit 6: Integration Techniques, L’Hopital’s Rule & Improper Integrals
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