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(pi) = 2 and int_0^(pi) [f(x)+f^('')(x)] sin x dx = 5 then 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

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

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(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