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Calc 2 6.2

 

<== Calculus 2
Number Question Answer
See the work

      1.      

 

Evaluate the indefinite integral                    
∫ sin^3(12x)(cos^4(12x))dx

 

(-cos(12x)^5/5*12)+cos(12x)^7/(7*12)+C   
The work

Point Cost: 3

2.

 

Evaluate the indefinite integral
∫ 43cos^3(18x)dx

 

43/18*sin(18x)-43/(3*18)*(sin(18x))^3+C
The work

Point Cost: 3

3.

 

 

 

a=(π/6)

b=0

∫ sin^4(6x)dx

 

0.196349540875
The work

4.

 

Evaluate the indefinite integral 
∫ 79cos^2(60x)dx

 

79*x/2+79*sin(2*60x)/(4*60)
The work

Point Cost: 3

5.

 

Evaluate the indefinite integral 
∫ xcos^2(4x)dx

 

(4x^2+xsin(2*4x)+(cos(2*4x)/(2*4)/(4*4))
The work

Point Cost: 3

6.

 

 

 

Evaluate the indefinite integral 

a=13

b=5

∫ sin^2(6x)cos^2(6x)dx

1.00735626385

 

The work

7.

 

Evaluate the indefinite integral 
∫ (10-sinx)/(cosx)

 

10ln(abs(sec(x)+tan(x)))-ln(abs(sec(x)))

 

The work

8.

 

Evaluate the integral 
∫ sec^2(x)tan^7(x)dx

 

(tan(x)^(7+1))/(7+1)+C
The work

9.

 

 

 

Evaluate the integral 

a=(5π/4)

b=0

∫ sec^4(t/5)dt

20/3

 

The work

10.

 

Evaluate the indefinite integral 
∫ tan^2(4x)dx

 

(tan(4x)/4)-x+C
The work

11.

 

Evaluate the indefinite integral 
∫ tan^4(5x)dx

 

(tan(5x)^3)/(3/3*5)-(tan(5x)/5)+x+C

 

The work

12.

 

Evaluate the indefinite integral 
∫ tan^3(2x)sec^5(2x)dx

 

(sec(2x)^7)/(7*2)-(sec(2*x)^5)/(5*2)+C

 

The work

13.

 

Evaluate the indefinite integral 
∫ (9-9tan^2x)/(-4sec^2x)dx

 

9sin(2x)/(2*-4)+C
The work

14.

 

 

 

Evaluate the indefinite integral 
∫ sin(4x)cos(7x)dx

Hint: Use the identity

(sinA)(cosB)=(1/2)[sin(A-B)+sin(A+B)]

 

(-1/2)(cos((4_7)*x)/(4+7)+cos((4-7)*x)/(4-7))          
The work

15.

 

 

 

 

 

 

 

 

For each of the indefinite integrals below,
choose which of the following substitutions would
be most helpful in evaluating the integral. Enter the
appropriate letter (A,B, or C)
in each blank. DO NOT EVALUATE THE INTEGRALS.        
A. x = 4tanø
B. x = 4sinø
C. x = 4secø


1. ∫ x^2(sqrt(16+x^2)dx
2. ∫ sqrt(x^2-16)dx
3. ∫ (x^2-16)^(5/2)dx
4. ∫ dx/(16+x^2)^3
5. ∫ dx/(16-x^2)^(3/2)

 

1. A

2. C

3. C

4. A

5. B

The work

16.

 

 

 

Evaluate the definite integral 

a=20sin(π/8)

b=0

∫ (x^3/(sqrt(400-x^2)))dx

45.1785265
The work

17.

 

 

Evaluate the definite integral 

a=7

b=0

∫ (x^3(sqrt(x^2+49)))dx

5410.09164570728
The work
18. Evaluate the indefinite integral 
∫ 10/(x^2*sqrt(324x^2-25))dx
10((324(x^2)-25)^(1/2))/(25x)
The work