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Calc 2 5.5

 

<== Calculus 2
Number Question Answer
See the work

1.

 

 

Evaluate the integral by making the given          
substitution
 u=   

 

-2*3*cos()

The work

Point Cost: 3

2.

 

 

 

Evaluate the integral 

 

by making the substitution u=x^4-2

 

(1/45)(1/4)(x^4 - 2)^45         
The work

Point Cost: 3

3.

 

 

Evaluate the indefinite integral

∫ (x^8)(e^(x^9))

 

.11111111111*(e^(x^9))
The work

Point Cost: 3

4.

 

 

Evaluate the indefinite integral

∫ ((ln(x))^5)/x

 

(ln(x)^6)/6
The work

Point Cost: 3

5.

 

 

Evaluate the indefinite integral

∫ (dx/(10-3x))

 

-ln(abs(10-3x))/3
The work

Point Cost: 3

6.

 

 

Evaluate the indefinite integral

∫ (1/(7t+8)^1.8)dt

 

(-(7t+8)^(-.8))/(7(.8))
The work

Point Cost: 3

7.

 

 

Evaluate the indefinite integral

∫ (x^3)sqrt(13+x^4)dx

 

(2/3)(1/4)(x^4+13)^(3/2)
The work

Point Cost: 3

8.

 

 

Evaluate the indefinite integral

∫ (arcsinx)^9/(sqrt(1-x^2))dx

 

(arcsin(x))^10/10
The work

Point Cost: 3

9.

 

 

Evaluate the indefinite integral

∫ (cos(4/x)/x^2)dx

 

(-sin(4/x))/4
The work

Point Cost: 3

10.

 

 

Evaluate the indefinite integral

∫ sin(9t)sec^2(cos(9t))dt

 

-tan(cos(9t))/9
The work

Point Cost: 3

11.

 

Evaluate the indefinite integral

A. ∫ (((3e^x)+6)/e^x)dx

B. ∫(e^x)/((3e^x)+6)dx

 

A. 3x-6e^-3

B. ln(3e^x+6)/3

The work

Point Cost: 3

12.

 

 

Evaluate the indefinite integral

∫ (5sinx+11tanx)dx

 

5(-cos(x))-11*ln(abs(cos(x)))
The work

Point Cost: 3

13.

 

 

Evaluate the indefinite integral

∫ (5sinx)/(1+cos(x)^2)dx

 

-5arctan(cos(x))
The work

Point Cost: 3

14.

 

 

Evaluate the indefinite integral

∫ (4x)/(x^4+1)dx

 

2(arctan(x^2))
The work

Point Cost: 3

15.

 

 

 

 

Evaluate the definite integral:

a=6

b=0 3

∫ x(sqrt(x+5))dx

 

161.4665522
The work

Point Cost: 3

16.

 

Evaluate the definite integral

a=(π/2)

b=(-π/2)

∫ ((2x^4sin(4x))/(1+x^8))dx

 

0
The work

17.

 

 

Evaluate the indefinite integral

∫ (x/(sqrt(1+x^8)))dx

 

2(x+8)*sqrt(x+8)/3-2*8*sqrt(x+8)+C   
The work

Point Cost: 3

18.

 

Evaluate the definite integral

a= e^5

b=e^3

∫ dx/(xsqrt(lnx))

 

1.00803434
The work

Point Cost: 3

19.

 

 

Evaluate the indefinite integral.

∫ ((9x+4)/(x^2+1))dx

 

4*arctan(x)+(1/2)*(9)*ln(x^2+1)
The work

Point Cost: 3

20.

 

Find the average value of ƒ(x)=cos(18x) on the
interval [0, π/2].

 

0
The work

Point Cost: 3

21.

 

Find the average value of ƒ(t)=-2te^(-t^2) on the
interval [0.9]

 

(e^(-9^2)-1)/9
The work

Point Cost: 3

22.

 

 

Find the average value of the function
ƒ(t)=cos^14(5t)sin(5t)
on the interval [2,9].

 

-0.00013715505895
The work

Point Cost: 3

23.

 

 

Find the average value of the function
ƒ(r)=(8)/(1+r)^2
on the interval [4,7]

 

0.2
The work

Point Cost: 3

24.

 

 

 

In omaha Nebraska the temperature in degrees Fahrenheit
t hours after 9am was approximated by the function
T(t)=80+15sin(πt/12)
Determine the temperature at 9 am___
Determine the temperature at 3 pm___
Find the average temperature during the period from 9 am to 9 pm.________

Temperature at 9: 80

Temperature at 3: 95

Average: 89.5493

The work

Point Cost: 3