Write your solutions clearly and legibly. No credit will be given for illegible 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

• 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 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

for full question see attachment