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Integrate with respect to x :

4x2.dx

4x2.dx

Evaluate

∫

dx ) 1- x(

2

(a) x

5

/5 – 2/3 x

3

+ x + k

(b)

kx

3

x

3

+−

(c) 2x

(d) none of these

5.

∫

+

) x 1 ( ) 3x –1 (

dx is equal to

(a) x – x

2

– x

3

(b) x

3

– x

2

+ x (c) x – x

2

– x

3

+ k (d) none of these

6.

[

]

∫

x/1–x

dx is equal to

(a)

3

2

x

3/2

– 2 x

½

+k (b)

kx2x

3

2

+−

(c)

k

xx2

1

x2

1

++

(d) none of these

7. The integral of px

3

+ qx

2

+ rk + w/x is equal to

(a) px

2

+ qx + r + k

(b) px

3

/3 + qx

2

/2 + rx

(c) 3px + 2q – w/x

2

(d) none of these

8. Use method of substitution to integrate the function f(x) = ( 4x + 5 )

6

and the answer is

(a) 1/28 ( 4x + 5 )

7

+ k (b) ( 4x + 5 )

7

/7 + k (c) ( 4x + 5 )

7

9. Use method of substitution to evaluate

∫

+

52

)4x(x

dx and the answer is

10. Integrate ( x + a )

n

and the result will be

∫

dx ) 1- x(

2

(a) x

5

/5 – 2/3 x

3

+ x + k

(b)

kx

3

x

3

+−

(c) 2x

(d) none of these

5.

∫

+

) x 1 ( ) 3x –1 (

dx is equal to

(a) x – x

2

– x

3

(b) x

3

– x

2

+ x (c) x – x

2

– x

3

+ k (d) none of these

6.

[

]

∫

x/1–x

dx is equal to

(a)

3

2

x

3/2

– 2 x

½

+k (b)

kx2x

3

2

+−

(c)

k

xx2

1

x2

1

++

(d) none of these

7. The integral of px

3

+ qx

2

+ rk + w/x is equal to

(a) px

2

+ qx + r + k

(b) px

3

/3 + qx

2

/2 + rx

(c) 3px + 2q – w/x

2

(d) none of these

8. Use method of substitution to integrate the function f(x) = ( 4x + 5 )

6

and the answer is

(a) 1/28 ( 4x + 5 )

7

+ k (b) ( 4x + 5 )

7

/7 + k (c) ( 4x + 5 )

7

9. Use method of substitution to evaluate

∫

+

52

)4x(x

dx and the answer is

10. Integrate ( x + a )

n

and the result will be

integral of( log x) power 2

integral of log x value is

Q. State and prove fundamental theorem of integral calculus.

Find the area of the region that lies inside the first curve and outside the second curve.

r2 = 18 cos 2θ, r = 3

r2 = 18 cos 2θ, r = 3

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ʃ1/(1-x)3dx

ʃ1/(1-x)3dx

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ʃ[x4/(x-1)(x+2)1/2]dx

ʃ[x4/(x-1)(x+2)1/2]dx

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ʃ(sinx+cosx/tanx)dx

ʃ(sinx+cosx/tanx)dx

Find the reduction formula of ʃsec6xdx.