int_(0)^( pi/2)x cot xdx

int_(0)^( pi/2)x sin xdx

" 4."int_(0)^( pi)x cos xdx=-2

" (3) "int_(x=0)^(pi/2)cos xdx

If f:[0,pi]rarr R is continuous and int_(0)^( pi)f(x)sin xdx=int_(0)^( pi)f(x)cos xdx=0 then the number of roots of f(x) in (0,pi) is ...

" (x) "int_(0)^( pi/4)tan xdx

int_(0)^(pi/2)(cot^(2)xdx)/(tan^(2)x+cot^(2)x)

int_(0)^((pi)/(2))x cos xdx

int_(0)^( pi/2)e^(x)xdx=

int_(0)^( pi/2)x sin x cos xdx