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

If int_0^oo x^(2n+1)\ e^(-x^2)\ dx=360, then the value of n is___

If int_0^1e^ (-x^2) dx=a , then find the value of int_0^1x^2e^ (-x^2) dx in terms of a .

Let I_1=int_0^1e^(x^2)dx and I_2=int_0^(1)2x^(2)e^(x^2)dx then the value of I_1 +I_2 is equal to

If int_0^1e^-x^2dx=a , then find the value of int_0^1x^2e^-x^2dx in terms of a .

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

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

If f(x)=int(3x^2+1)/((x^2-1)^3)dxa n df(0)=0, then the value of |2/(f(2))| is___

If f(x)=int(3x^2+1)/((x^2-1)^3)dxa n df(0)=0, then the value of |2/(f(2))| 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.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 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