`overset(pi)underset(0)int(x)/(1+sinx)dx`.

The value of the integral overset(pi)underset(0)int (sin k x)/(sin x)dx (k is an even integer) is equal to

overset(pi)underset(0)int (1)/(1+3^(cosx)) dx is equal to

The value of overset(16pi//3)underset(0)int |sinx|dx is

The value of the integral overset(pi)underset(0)int log(1+cos x)dx is

The value of the definite integral overset(3pi//4)underset(0)int(1+x)sin x+(1-x) cos x)dx is

The value of overset(3pi//4)underset(pi//4)int (x)/(1+sin x) dx is equal to

If I=overset(1)underset(0)int (1)/(1+x^(pi//2))dx then

Consider the integrals I_(1)=overset(1)underset(0)inte^(-x)cos^(2)xdx,I_(2)=overset(1)underset(0)int e^(-x^(2))cos^(2)x dx,I_(3)=overset(1)underset(0)int e^(-x^(2//2))cos^(2)xdx and I_(4)=overset(1)underset(0)int e^(-x^(2//2))dx . The greatest of these integrals, is

Let overset(a)underset(0)int f(x)dx=lambda and overset(a)underset(0)int f(2a-x)dx=mu . Then, overset(2a)underset(0)int f(x) dx equal to

If I_(1)=overset(1)underset(0)int 2^(x^(2)) dx, I_(2)=overset(1)underset(0)int 2^(x^(3)) dx, I_(3)=overset(2)underset(1)int 2^(x^(2))dx and I_(4)=overset(2)underset(1)int 2^(x^(3))dx then