webwork4.pdf - Margarita Christoff BB WeBWorK assignment...

Margarita Christoff BB
WeBWorK assignment due : 10/12/2018 at 11:59pm EDT.
1. (1 point) Use integration by parts to find the following:
Z
xe
3 x
d x = .
Hint: Use the substitution
u = x and d v = e
3 x
d x
(2 points) Evaluate the following definite integrals:
(a)
R
1
0
x
2
e
x
dx = .
(b)
R
1
0
x
2
2
x
dx = .
(c)
R
2
1
( ln ( x ))
2
dx = .
(d)
R
π
2
0
cos
6
( x ) dx = .
2. (1 point) Evaluate the definite integral.
5. (2 points) Evaluate the following definite integrals:
(a)
R
1
0
x
2
e
x
dx = .
(b)
R
1
0
x
2
2
x
dx = .
(c)
R
2
1
( ln ( x ))
2
dx = .
(d)
R
π
2
0
cos
6
( x ) dx = .
Z
7
t
2
ln ( 5 t ) dt
Answer(s) submitted:
• 0
(incorrect)
3. (1 point) Use integration by parts to find the following:
Z
( t + 7 ) e
2 t + 3
d t = .
Hint: Use the substitution
u = t + 7 and d v = e
2 t + 3
d x
4. (1 point) Use integration by parts to find the following:
Z
x sin2 x d x = .