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

Evaluate int_0^(pi/2) xcosx dx

int_0^(pi/2) cos^5xdx

Evaluate: int_0^(pi/2) xcotx dx

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

int_0^(pi/2) sinxcos^3xdx

(i) int_0^(pi/2) sin^2 x dx (ii) int_0^(pi//2) cos^2 x dx

int_0^(pi/2) x^2sinxdx

int_(0)^(pi//2)xcosxdx =?

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