# Mathematics solutions

Mathematics solutions

I have these 3 other questions i also need. Are you available? I could only pay 15.00 seeing as thats the last that i have. Attached is the file i would only need 2,3, and 5
INSTRUCTIONS
• 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
imaginary numbers.
2
3. (10 points) Simplify and express
(

1

2
+
1

2
ı
)
2+2ı
as a complex number a + bı, where a and b are real numbers.
4. (10 points) Find M6
for

3
−3
ln(x
2
+ 1) dx.
3
5. (10 points) Evaluate

x
3
+ 1
x(x
2
− 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
T
N =

b
a
f (x) dx
for all N and all endpoints a, b.
SURVEY QUESTION (5 EXTRA CREDIT POINTS):
To be determined.
6

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