Home
Class 12
MATHS
Let int(x^(2))/(sqrt(1-x))dx=psqrt((1-x)...

Let `int(x^(2))/(sqrt(1-x))dx=psqrt((1-x))(3x^(2)+4x+8),` then value of p is

A

`(-2)/(15)`

B

`(2)/(15)`

C

`(4)/(15)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`int(x^(2))/(sqrt(1-x))dx=psqrt((1-x))(3x^(2)+4x+8)`
Put `1-x=t^(2)` in LHS, we get
`l=-int(2t)/(t)(1-t^(2))^(2)dt=-2 int(1+t^(4)-2t^(2))dt`
`=-2[t+(t^(5))/(5)-(2t^(3))/(3)]`
`=-2sqrt(1-x)[1+((1-x)^(2))/(5)-(2)/(3)(1-x)]`
`=-2sqrt(1-x)[(15+3(1+x^(2)-2x)-10(1-x))/(15)]`
`=(-2)/(15)sqrt(1-x)(3x^(2)+4x+8)`
But `l=psqrt(1-x)(3x^(2)+4x+8)`
`therefore" "p=(-2)/(15)`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

  • LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

Similar Questions

Explore conceptually related problems

int(x^(2)-1)/(x sqrt(1+x^(4)))dx

int((2x-1)^(2)(x+3))/(sqrt(x))dx

int(1)/(sqrt(8+2x-x^(2)))dx=

int(2x+3)/sqrt(1+x+x^2)dx

int(1)/(sqrt(4x^(2)-4x+3))dx=

int(2x)/(sqrt(1-x^(2)-x^(4)))dx=

Let int(x^((1)/(2)))/(sqrt(1-x^(3)))dx=(2)/(3)g(f(x))+c then

int(2x)/(sqrt(1-x^(2)-x^(4)))dx

int(1)/(sqrt(4+8x-5x^(2)))dx

int(1)/(sqrt(5-4x-2x^(2)))dx