`int_0^pi xsinxcos^4x dx`

int_0^pi sin^4x cos^4x dx

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

Prove that: int_0^(pi//2) cos^4 x dx =(3pi)/16

int_(0)^(pi) xsin x cos^(4)x dx=

Evaluate: int_0^pi |cos x| dx

int_0^pi (cos^2x)dx ,

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

Evaluate (i) int_0^pi (x sin x)/(1+cos^2 x) dx Evaluate (ii) int_0^pi (4x sin x)/(1+ cos^2 x) dx