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).`

f(x) = sinx - sin2x in [0,pi]

Let f(0)=f'(0)=0 and f^(primeprime)(x)=sec^4x+4 then find f(x)

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 is continuous on [0,1] such that f(x)+f(x+1/2)=1 and int_0^1f(x)dx=k , then value of 2k is 0 (2) 1 (3) 2 (4) 3

The integral int_(0)^(pi//2) f(sin 2 x)sin x dx is equal to

If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove that int_0^(2a)f(x)dx=int_0^a{f(x)+(2a-x)}dx

The value of the integral int_(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/(2))=-(3pi^(2))/(4) , then lim_(xto -pi^+) (f(x))/(sin(sinx)) is equal to