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Calc 2 6.6

 

<== Calculus 2
Number Question Answer
See the work

1.

 

 

 

Find the area under the curve y=1/(2x^3) from x=1
to x = t and evaluate it for t = 10; t = 100. Then
find the total area under this curve for x>= 1.

a. t=10
b. t=100
c. total area

 

a. 0.2475
b. 0.249975
c. 0.25
The work

Point Cost: 3

2.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a= ∞ b= 2 ∫ 8/((x+3)^(3/2))dx

 

4.472136
The work

Point Cost: 3

3.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a= -2 b= inf int 1/(sqrt(2-w))dw

 

Divergent
The work

Point Cost: 2

4.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a= 1 b=- ((2)/(2x-3)^2)dx

 

4
The work

Point Cost: 3

5.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a= b= 0 7e^(-x)dx

 

5
The work

Point Cost: 2

6.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a= -5 b=  e^(-5t)dt

 

Divergent
The work

Point Cost: 2

7.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a=  b= 5π sin(5ø)dø

 

Divergent
The work

Point Cost: 2

8.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a= b=  (-4x^4)dx

 

Divergent
The work

Point Cost: 2

9.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If it diverges to infinity,
answer infinity. If it diverges to negative infinity, answer negative
infinity.

 

Negative Infinity
The work

Point Cost: 2

10.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a= b= 3 (ln(x)/x) dx

Divergent
The work

Point Cost: 2

11.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a=  b= 1 (8lnx)/x^8 dx

 

9
The work

Point Cost: 3

12.

 

 

 

Determine whether the integral is divergent or convergent.             
If it is convergent, evaluate it. If not, state your answer
as divergent
a=  b= 9x^2/(1+x^6) dx

 

6.28319
The work

Point Cost: 4

13.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a= 11 b= 4 11/(x-4)^(1/3) dx

 

49.40063      
The work

Point Cost: 4

14.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it.
a=9 b=1.5 -4/(x-5)^3 dx

 

Divergent
The work

Point Cost: 1

15.

 

 

 

Determine whether the integral is divergent or convergent.
If it is convergent, evaluate it. If not, state your answer
as divergent
a= 1<br /> b= 0<br /> ∫ 8/(sqrt(1-x^2)) dx

 

12.56637
The work

Point Cost: 3

16.

 

 

Determine whether the integral is divergent or convergent.
a= 5 b= 0 1/(x^0.3) dx

 

4.898979
The work

Point Cost: 3

17.

 

 

Determine whether the integral is divergent or convergent.
a=   b= 9 1/x^(9/8) dx

 

7.375327
The work

Point Cost: 4