If `int_0^oox^(2n+1)dote^(-x^2)dx=360 ,` then the value of `n` is___

The value of int_0^oox^(2n+1)dote^(-x^2)dx is (n in W)

Statement I int_(0)^(1)2^(x)x^(2)dx=(2)/(ln2)-(4)/((ln2)^(2))+(2)/((ln2)^(3)) Statement II int_(0)^(1)e^(x)(x-1)^(n)dx=16-6e then the value of n is 3 .

If A=int_0^1 x^50(2-x)^50dx, B=int_0^1 x^50(1-x)^50dx and A/B=2^n , then the value of n is …

If I_(n)=int_(0)^(2)(2dx)/((1-x^(n))) , then the value of lim_(nrarroo)I_(n) is equal to

If M=int_(0)^((pi)/2)(cosx)/(x+2)dx and N=int_(0)^((pi)/4)(sinxcosx)/((x+1)^(2))dx , then the value of M-N is

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.For example, int_0^1 x^3 (1-x)^4dx=int_0^1 x^(4-1) (1-x)^(5-1) dx=beta(4,5) and int_0^1 x^(3/2) (1-x)^((-1)/2)dx=int_0^1 x^(5/2-1) (1-x)^(1/2-1)dx=beta(5/2,1/2) .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.For example, int_0^1 x^3 (1-x)^4dx=int_0^1 x^(4-1) (1-x)^(5-1) dx=beta(4,5) and int_0^1 x^(3/2) (1-x)^((-1)/2)dx=int_0^1 x^(5/2-1) (1-x)^(1/2-1)dx=beta(5/2,1/2) .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

int x ^ (2n-1) cos x ^ (n) dx

For every integer n, int_(n)^(n+1)f(x)dx=n^(2) , then the value of int_(0)^(5)f(x)dx=