Review problems for the final exam

| August 30, 2017

Question
151 Review problems for the final exam
Try to do all the problems before you watch the video solution.
Note: The material covered in this set of problems doesn’t contain the material for the first
and the second exam.

3

1. A continuous function f (x) is such that
0

f (x)dx = −4 and


5

0

f (x)dx = −10.

5

f (x)dx.

Find
3

2. Evaluate each of the given integrals.

3 +4

x2 ex

(a)

dx

(b)

sin x cos xdx

(c)

t2
dt
t−1

3. Find the area of the region that is enclosed between the curves y = 2x and y = x2 − 3.

4. Evaluate each of the given integrals.

(a)

(b)

ex
dx
1 + e2x
e2x
dx
1 + e2x

5. Let F (x) =

x

t2 cos (et + 1)dt.

5

d
F (x).
dx
(b) Evaluate F (5).
(a) Find

c
⃝Sara Nadiv Soffer

Prepared by Sara Nadiv Soffer
1

6. Evaluate each of the definite integrals.

(a)

π

x sin x2 dx

0

3

(b)
1

dx
dx
3x + 1

7. Evaluate x→∞
lim

∫x

8. Find lim
+
x→0

0

n
∑ 2k(k + 1)
k=1

n3

sin (t3 )dt
.
x4

c
⃝Sara Nadiv Soffer

Prepared by Sara Nadiv Soffer

2

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