`int_0^(pi/2) e^-xcosxdx`

Evaluate: int_0^(pi/2)xcosx dx

Evaluate the definite integrals int_0^(pi/2) cos2xdx

int_0^(pi/2) cos^5xdx

Evaluate: int_0^(pi//2)cosx\ dx

Evaluate: int_0^(pi/2)xcotx dx

The value of int_0^(pi/2)cos^2xdx

Evaluate the definite integrals int_0^(pi/2)cos^2xdx

Let I_1=int_0^(pi/2)(dt)/(1+t^6)and I_2int_0^(pi/2)(xcosxdx)/(1+(xsinx+cosx)^6), then

int_0^(pi/2) sin^2xcos^2xdx

Consider I_1=int_0^(pi//4)e^(x^2)dx ,I_2=int_0^(pi//4)e^x dx ,I_3=int_0^(pi//4)e^(x^2)cosxdx , I_4=int_0^(pi//4)e^(x^2)sinxdx . STATEMENT 1 : I_2> I_1> I_3> I_4 STATEMENT 2 : For x in (0,1),x > x^2a n dsinx >cosx .