[" 53.Let "f" be the function on "[-pi,pi]" given by "f(0)=9" and "f(x)=sin((9x)/(2))/sin((x)/(2))" for "x!=0" .The real "],[(2)/(pi)int_(-pi)^( pi)f(x)dx" is : "]

Let f be the function defined on [-pi,pi] given by f(0)=9 and f(x)=sin((9x)/2)/sin(x/2) for x!=0 . The value of 2/pi int_-pi^pif(x)dx is

Let f be the function defined on [-pi,pi] given by f(0)=9 and f(x)=sin((9x)/2)/sin(x/2) for x!=0 . The value of 2/pi int_-pi^pif(x)dx is

Let f be the function defined on [-pi,pi] given by f(0)=9 and f(x)=sin((9x)/2)/sin(x/2) for x!=0 . The value of 2/pi int_-pi^pif(x)dx is (asked as Match the following question)

int_(-pi)^( pi)sin x[f(cos x)]dx is equal to

Prove that the function f given by f(x) = log sin x is increasing on (0, (pi)/(2)) and decreasing on ((pi)/(2),pi) .

int_(0)^( pi)xf(sin x)dx=(pi)/(2)int_(0)^( pi)f(sin x)dx

Prove that the function f given by f(x) = log sin x is increasing on (0,(pi)/(2)) and decreasing on ((pi)/(2),pi) .

Prove that the function f given by f(x) = log sin x is increasing on (0,(pi)/(2)) and decreasing on ((pi)/(2),pi) .

Prove that the function f given by f(x) = log sin x is increasing on (0,(pi)/(2)) and decreasing on ((pi)/(2),pi) .

If f(x)=(sin x)/(x)AA x in(0,pi], prove that (pi)/(2)int_(0)^((pi)/(2))f(x)f((pi)/(2)-x)dx=int_(0)^( pi)f(x)dx