Home
Class 12
MATHS
int(3x^2)/sqrt(9-16x^6)dx...

`int(3x^2)/sqrt(9-16x^6)dx`

A

`(1)/(4)sin^(-1)((x^(3))/(3))+C`

B

`(1)/(4)sin^(-1)((4x^(3))/(3))+C`

C

`4sin^(-1)((x^(3))/(4))+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put `x^(3)=t and 3x^(2)dx=dt. `
`therefore I=int(dt)/(sqrt(9-16t^(2)))=(1)/(4)int (dt)/(sqrt((9)/(16)-t^(2)))=(1)/(4).int(dt)/(sqrt(((3)/(4))^(2)-t^(2)))`
`=(1)/(4)sin^(-1) ""(t)/(((3)/(4)))+C=(1)/(4)sin^(-1)((4x^(3))/(3))+C.`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION USING PARTIAL FRACTIONS

    RS AGGARWAL|Exercise Objective Questions I|32 Videos

  • INDEFINITE INTEGRAL

    RS AGGARWAL|Exercise Objective Questions|41 Videos

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Objective Questons|57 Videos

Similar Questions

Explore conceptually related problems

int(x^(2))/(9+16x^(6))dx

int(x)/(sqrt(9-x^(2)))dx

If int(1)/(sqrt(9-16x^(2)))dx=alphasin^(-1)(betax)+c , then alpha+(1)/(beta)=

(i) int(sinx)/(sqrt(4+ cos^(2) x)) dx " "(ii) int(x^(2))/(sqrt(9+x^(6)))dx

int(x+3)/(sqrt(9-x^(2)))dx

int(x)/(sqrt(9+x^(2)))dx

int(dx)/(sqrt(16-x^(2)))

int(dx)/(sqrt(9-4x^(2)))

if int (1)/(sqrt(9-16x^(2)))dx=alpha sin ^(-1) (beta x) +c. then alpha +(1)/(beta )=

int(dx)/(sqrt(9-25x^(2)))