Home
Class 12
MATHS
Find the value of int(0)^(1)x(1-x)^(n)dx...

Find the value of `int_(0)^(1)x(1-x)^(n)dx`.

Text Solution

Verified by Experts

`int_(0)^(1)x(1-x)^(n)dx`
`=int_(0)^(1)(1-x).{1-(1-x)}^(n)dx`
`=int_(0)^(1)(1-x).x^(n)dx`
`=int_(0)^(1)(x^(n)-x^(n+1))dx`
`=[(x^(n+1))/(n+1)-(x^(n+2))/(n+2)]_(0)^(1)`
`=(1)/(n+1)-(1)/(n+2)=(1)/((n+1)(n+2))`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|44 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.10|10 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

Evaluate : int_(0)^(1)x(1-x)^(n)dx

Find the value of int_0^1x(1-x)dx

Find the value of int_(0)^(1)root(3)(2x^(3)-3x^(2)-x+1)dx .

If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0 , then find the value of int_(0)^(a)(dx)/(1+f(x)) .

The value of int_(0)^(1) (1)/(2x-3)dx is

Find the value of int_(0)^(2pi)1/(1+tan^(4)x)dx

If f:RrarrR defined by f(x)=sinx+x , then find the value of int_0^pi(f^-1(x))dx

Evaluate : int_(0)^(1) (1-x)^(3//2) dx

If f(x)={(1-|x| ,, |x|lt=1),(0 ,, |x|>1):} and g(x)=f(x-1)+f(x+1), then find the value of int_(-3)^5g(x)dx .

Evaluate : int_0^1x(1-x)^5dx