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

If f(pi)=2 and int_(0)^(pi)(f(x)+f''(x))sin x dx=5 , then f(0) is equal to ( it is given that f(x) is continuous in [0,pi] )

If f(pi)=2 and int_(0)^(pi)(f(x)+f''(x))sin x dx=5 , then f(0) is equal to ( it is given that f(x) is continuous in [0,pi] )

If f(pi)=2 and int_(0)^(pi)(f(x)+f''(x))sinx dx=5 then f(0) is equal to, (it is given that f(x) is continuous in [0,pi] )

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

Let R to R be a differentiable functions such that its derivative f' is continuous and f(pi) = - 6 . If F : [0,pi] to R is defined by F(x) int_(0)^(x) f(t) dt , and int_(0)^(x) f(t) dt and if int_(0)^(pi) (f'(x) +F(x))cos xdx = 2 then the value of f(0) is _________

int_(0)^(pi) x f (sin x) dx is equal to