Question
Transcribed Text
Problem 1:
Evaluate the integral Z
x
2 − x + 1
x − 2
dx using polynomial long division.
a.) Use long division to break apart the integrand into a polynomial and a remainder.
b.) Evaluate the broken up integrand you found above.
Problem 2:
Rewrite the integrand of the integral Z
1
x
2 + 3x − 3
dx by completing the square.
a.) Complete the square for the polynomial in the denominator.
b.) (Extra) Use a trigonometric substitution to evaluate the integral (Hint: use two
successive u-subs).
1
2
Problem 3:
Determine whether the following statements are true or false and give an explanation or
counterexample:
a.) Z
uv0
dx =
Z
udx Z
v
0
dx
.
b.) Z
uv0
dx = uv −
Z
vu0
dx.
c.) Z
vdu = uv −
Z
udv.
Problem 4:
Evaluate the integral Z π
0
x cos(x)dx:
Problem 5:
Evaluate the integral Z
x ln2
(x)dx:
Problem 6:
Use trigonometric identities to evaluate the integral Z
sin3
(x) cos2
(x)dx:
Problem 7:
Use a trigonometric substitution to evaluate the integral Z
x
2
16 + x
2
dx:
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