The value of difinite integral int(0)^(1...

The value of difinite integral `int_(0)^(1)=(dx)/(sqrt((x+1)^(3)(3x+1)))` equals

A

`sqrt2-1`

B

`tan.(pi)/(12)`

C

`tan.(5pi)/(12)`

D

none of these

Verified by Experts

The correct Answer is:

A

`I=int_(0)^(1)(dx)/((x+1)sqrt((x+1)(3(x+1)-2)))`
Put `x+1=(1)/(t)`
`therefore" "I=int_(1)^(1//2)(dt)/(sqrt(3-2t))=sqrt2-1`

Similar Questions

Explore conceptually related problems

The value of definite integral int _(0)^(oo) (dx )/((1+ x^(9)) (1+ x^(2))) equal to:

The value of the integral int_(0)^(1) x(1-x)^(n)dx is -

The value of the definite integral int_(-1)^(1)(1+x)^(1//2)(1-x)^(3//2)dx equals

The value of the integral int_(-1)^(1) (x-[2x]) dx,is

The value of the integral int_(0)^(a) (1)/(x+sqrt(a^(2)-x^(2)))dx , is

If the value of the integral I=int_(0)^(1)(dx)/(x+sqrt(1-x^(2))) is equal to (pi)/(k) , then the value of k is equal to

The value of the integral int_(0)^(1) (1)/((1+x^(2))^(3//2))dx is

The value of the integral int _0^oo 1/(1+x^4)dx is

Evaluate the definite integrals int_0^1 (dx)/(sqrt(1+x)-sqrt(x))