`Iff(pi)=2int_0^pi(f(x)+f^(x))sinxdx=5,t h e nf(0)` is equal to (it is given that `f(x)` is continuous in `[0,pi])dot` 7 (b) 3 (c) 5 (d) 1

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equal to (a) -cosx (b) -sinx (c) int_0^x(x-t)f(t)dt (d) 0

f(x)=sinx+int_(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The range of f(x) is

If f(0)=1,f(2)=3,f(2)=5,t h e nfin dt h ev a l u eof int_0^1xf"(2x)dx

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dxdot

If int_(0)^(x)f(x)sint dt=" constant, " 0 lt x lt 2pi and f(pi)=2 , then the value of f(pi//2) is

Iff(2-x)=f(2+x)a n df(4-x)=f(4+x) for all xa n df(x) is a function for which int_0^2f(x)dx=5,t h e nint_0^(50)f(x)dx is equal to 125 (b) int_(-4)^(46)f(x)dx int_1^(51)f(x)dx (d) int_2^(52)f(x)dx

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"