`int_0^(pi//2)xsinx dx`

int_0^(pi/2) sin x dx

Evaluate : int_0^(pi/2) x sinx dx

int_0^(pi/2) sin^6x dx

Evaluate the following definite integrals: int_0^(pi//2)xsinx sin2x dx

Evaluate: int_0^(pi//2)(xsinx cos\ x)/(sin^4x+cos^4x)dx

Prove that: int_0^(pi//2)logsinx\ dx=\ int_0^(pi//2)logcosx\ dx=-pi/2log2

(i) int_0^(pi//2) sin^2 dx =pi/4 (ii) int_0^(pi//2) cos^2x dx=pi/4 (iii) int_(-pi//4)^(pi//4) sin^2 x dx=pi/4-1/2 (iv) int_(-pi//4)^(pi//4) cos^2x dx=pi/4+1/2

int_0^(pi//2) sin^3 x dx

Evaluate int_0^(pi/2) xcosx dx

(i) int_0^(pi//2) cos x dx (ii) int_(-pi//2)^(pi//2) cos x dx (iii) int_0^(pi//2) cos 2x dx