If f(x) is continuous in `[0,pi]` such that `f(pi)=3 and int_0^(pi/2)(f(2x)+f^(primeprime)(2x))sin2x dx=7` then find `f(0).`

If f(x) is continuous in [0,pi] such that f(pi)=3 and int_(0)^((pi)/(2))(f(2x)+f'(2x))sin2xdx=7 then find f(0)

If f(x) is twice differentiable in x in[0,pi] such that f(0)=f(pi)=0 and int_(0)^((pi)/(2))(f(2x)+f'(2x))sin x cos xdx=k pi ,then k is

If f(pi)=2 and int_(0)^( pi)(f(x)+f'(x))sin xdx=5 then f(0) is equal to

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

int_(0)^(pi//2)(f(sec x))/(f(sec x)+f(cosec x))dx=

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

underset is If int_(0)^( pi)xf(sin x)dx=A int_(0)^((pi)/(2))f(sin x)dx, then A

If int_(0)^(pi)x f(sin x) dx = a int_(0)^(pi)f (sin x) dx , then a =

If f(x) is continuous at x = (pi)/2 , where f(x) = (sinx)^(1/(pi-2x)), "for" x != (pi)/2 , then f((pi)/(2)) =