Home
Class 12
MATHS
int(sqrt(3))^(sqrt(8))xsqrt(1+x^(2))dx=?...

`int_(sqrt(3))^(sqrt(8))xsqrt(1+x^(2))dx=?`

A

`(19)/(3)`

B

`(19)/(6)`

C

`(38)/(3)`

D

`(9)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Put `(1+x^(2))=t` and `2xdx=dt`.
`[x=sqrt(3)impliest=4]` and `[x=sqrt(8)impliest=9]`
`:. I=int_(4)^(9)sqrt(t)dt=[(1)/(2)xx(2)/(3)t^(3//2)]_(4)^(9)=(1)/(3)(27-8)=(19)/(3)`.
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    RS AGGARWAL|Exercise Exercise 16D|17 Videos

  • CROSS,OR VECTOR, PRODUCT OF VECTORS

    RS AGGARWAL|Exercise Exercise 24|26 Videos

  • DETERMINANTS

    RS AGGARWAL|Exercise Objective Questions|29 Videos

Similar Questions

Explore conceptually related problems

Evaluate : int_(sqrt(8))^(sqrt(80)) x sqrt( 1+ x^2 ) dx =

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

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

int_(0)^(1/sqrt2)(dx)/(sqrt(1-x^(2)))

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

int_(0)^(1)x^(3)sqrt(1-x^(2))dx=

int_(0)^(1)x^(3)sqrt(1-x^(2))dx=

int_sqrt8^sqrt80xsqrt(1+x^2)dx=

int(1)/(sqrt((8)/(3)x-x^(2)))dx

int(1)/(x.sqrt(1-x^(3)))dx=