Home
Class 12
MATHS
Evaluate of each of the following integr...

Evaluate of each of the following integral: `int_a^b(x^(1//n))/(x^(1//n)+(a+b-x)^(1/n))dx ,\ n N ,\ ngeq2`

Text Solution

Verified by Experts

Let `I=int_a^b(x^(1//n))/(x^(1//n)+(a+b-x)^(1/n))dx`
By property
`int_a^bf(x)dx=int_a^bf(a+b-x)dx`
`I=int_a^b((a+b-x)^(1//n))/((a+b-x)^(1//n)+(x)^(1/n))dx...(2)`
(1)+(2)
`2I=int_a^b dx`
`2I=[x]_a^b`
`I=(b-a)/2`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA|Exercise Solved Examples And Exercises|277 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following integral: int_0^1x t a n^(-1)x\ dx

Evaluate the following Integrals : int (dx)/(x(x^(n)+1))

Evaluate the following integrals : (d) int ( x^( n-1) )/( x^( 2n) + a^(2) ) dx ,

Evaluate the following integrals: (1-35)pi/2int_(0)^( pi/2)(sin^(n)x)/(sin^(n)+cos^(n)x)dx

int (x ^(n-1))/( x ^(2n) + a ^(2)) dx =

The value of the integral int(dx)/(x^(n)(1+x^(n))^(1//n)), n in N is

The value of the integral int_0^1 x(1-x)^n dx=

int(dx)/(x^(n)(1+x^(n))^((1)/(n)))