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

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

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

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 overset(4)underset(-1)int f(x)=4 and overset(4)underset(2)int (3-f(x))dx=7 , then the value of overset(-1)underset(2)int f(x)dx , is

Given overset(2)underset(1)inte^(x^(2))dx=a , the value of overset(e^(4))underset(e )int sqrt(log_(e )x)dx , is

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

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

overset(pi//2)underset(-pi//2)int (cos x)/(1+e^(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

Let I_(1)=int_(1)^(2)(x)/(sqrt(1+x^(2)))dx and I_(2)=int_(1)^(2)(1)/(x)dx .Then