If `mgt0, ngt0`, the definite integral `I=int_0^1 x^(m-1)(1-x)^(n-1)dx` depends upon the values of `m` and `n` is denoted by `beta(m,n)`, called the beta function.Obviously, `beta(n,m)=beta(m,n)`.Now answer the question:If `int_0^2 (8-x^3)^((-1)/3)dx=kbeta(1/3,2/3)`, then `k` equals to (A) `1` (B) `1/2` (C) `1/3` (D) `1/4`

If mgt0, ngt0 , the definite integral I=int_0^1 x^(m-1)(1-x)^(n-1)dx depends upon the values of m and n is denoted by beta(m,n) , called the beta function.Obviously, beta(n,m)=beta(m,n) .Now answer the question:If int_0^oo x^(m-1)/(1+x)^(m+n)dx=k int_0^oo x^(n-1)/(1+x)^(m+n)dx , then k is equal to (A) m/n (B) 1 (C) n/m (D) none of these

If mgt0, ngt0 , the definite integral I=int_0^1 x^(m-1)(1-x)^(n-1)dx depends upon the values of m and n is denoted by beta(m,n) , called the beta function.Obviously, beta(n,m)=beta(m,n) .Now answer the question:The integral int_0^(pi/2) cos^(2m)theta sin^(2n)theta d theta= (A) 1/2beta(m+1/2,n+1/2) (B) 2beta(2m,2n) (C) beta(2m+1,2n+1) (D) none of these

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

Let I_(n) = int_(0)^(1)(1-x^(3))^(n)dx, (nin N) then

If I=int_(0)^(16)(x^((1)/(4)))/(1+sqrtx)dx=k+4tan^(-1)m , then 3k-m is equal to

The value of the definite integral int_0^(pi/2) ((1+sin3x)/(1+2sinx)) dx equals to

If I_(m,n)= int_(0)^(1) x^(m) (ln x)^(n) dx then I_(m,n) is also equal to

If the value of the definite integral int_0^1(sin^(-1)sqrt(x))/(x^2-x+1)dx is (pi^2)/(sqrt(n)) (where n in N), then the value of n/(27) is

Evaluate: int_0^1(x t a n^(-1)x)/((1+x^2)^(3//2))dx

Integrate int((x^(2n)-x^(2n-3)))/((2x^(3)+1)^(n))dx .