Write your solutions clearly and legibly. No credit will be given for illegible solutions.
Caiden
practice_midterm2v1.pdf
NAME:
SECTION:
MATH 20B MIDTERM #2
VERSION 1
INSTRUCTIONS
• Read each question carefully, and answer each question completely. • Show all of your work. No credit will be given for unsupported answers. • Write your solutions clearly and legibly. No credit will be given for
illegible solutions.
1. (10 points) Evaluate ∫ 1 0
e √ x
√ x
dx or state that it diverges.
# PTS
1
2
3
4
5
6
B
S
Σ
2. (10 points) Evaluate ∫
xe−2x sin(2x) dx. You may leave your answer as unsimplified complex exponentials—that is, your final answer may contain imaginary numbers.
2
3. (10 points) Simplify and express ( −
1 √ 2 +
1 √ 2 ı
)2+2ı as a complex num-
ber a + bı, where a and b are real numbers.
4. (10 points) Find M6 for ∫ 3 −3
ln(x2 + 1) dx.
3
5. (10 points) Evaluate ∫
x3 + 1
x(x2 − 1) dx
4
6. (10 points) Find the area of the inner loop of the limaçon r = 2 cos θ −1 pictured below.
0.5 1.0 1.5 2.0 2.5 3.0
-1.5
-1.0
-0.5
0.5
1.0
1.5
5
BONUS QUESTION (5 EXTRA CREDIT POINTS):
Show that if f(x) = rx + s is a linear function (r, s constants) then
TN = ∫ b a f(x) dx
for all N and all endpoints a, b.
SURVEY QUESTION (5 EXTRA CREDIT POINTS):
To be determined.
6
