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Integral Calculus

Integrate with respect to x :

4x2.dx

4x2.dx

Integral Calculus

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 Calculus

integral of( log x) power 2

Integral Calculus

integral of log x value is

Integral Calculus

Q. State and prove fundamental theorem of integral calculus.

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

Integral Calculus

Q. Intigrate

ʃ1/(1-x)3dx

ʃ1/(1-x)3dx

Integral Calculus

Q. Intigrate

ʃ[x4/(x-1)(x+2)1/2]dx

ʃ[x4/(x-1)(x+2)1/2]dx

Integral Calculus

Q. Intigrate

ʃ(sinx+cosx/tanx)dx

ʃ(sinx+cosx/tanx)dx

Integral Calculus

Find the reduction formula of ʃsec6xdx.