The value of `("^n C_0)/n`+`("^nC_1)/(n+1)`+`("^nC_2)/(n+2)`+....+`("^nC_ n)/(2n)` is equal to a.`int_0^1x^(n-1)(1-x)^n dx` b. `int_1^2x^n(x-1)^(n-1)dx` c. `int_1^2x^(n-1)(1+x)^n dx` d. `int_0^1(1-x)^(n-1)dx`

The value of (^nC_(0))/(n)+(^nC_(1))/(n+1)+(^nC_(2))/(n+2)+....+(n)/(2n) is equal to a.int_(0)^(1)x^(n-1)(1-x)^(n)dxbint_(1)^(2)x^(n)(x-1)^(n-1)dxc*int_(1)^(2)x^(n-1)(1+x)^(n)dx d.int_(0)^(1)(1-x)^(n-1)dx

evaluate int_(0)^(1)x^(2)(1-x)^(n)dx

If I(m,n)=int_0^1x^(m-1)(1-x)^(n-1)dx , then

int_(n)^(n+1)f(x)dx=n^(2)+n then int_(-1)^(1)f(x)dx=

The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(n))/(2n) (a) underset(0)overset(1)intx^(n-1)(1+x)^(n)dx (b) underset(1)overset(2)intx^(n)(x-1)^(n-1)dx (c) underset(1)overset(2)int(1+x)^(n)dx (d) underset(0)overset(1)int(1-x)^(n)x^(n-1)dx

What is int_0^1 x(1-x)^n dx equal to

int_n^(n+1)f(x) dx=n^2+n then int_(-1)^1 f(x) dx =

Prove that for ngt1 . int_0^1(cos^-1x)^ndx=n(pi/2)^(n-1)-n(n-1)int_0^1(cos^-1x)^(n-2)dx