Find `f(x)` which satisfies `f(x)=x+int_0^(pi/2) sinx*cosy*f(y)dy`

Find the function f(x) if it satisfies the condition f(x)=x+int_0^(pi//2)sin(x+y)f(y)dydot then find 'f(x)

The function f(x), that satisfies the condition f(x) = x + int_0^(pi//2) sinx . Cosyf(y) dy, is :

The function f(x), that satisfies the condition f(x) = x + int_0^(pi//2) sinx . Cosyf(y) dy, is :

Find f(x) if it satisfies the relation f(x)=e^(x)+int_(0)^(1)(x+ye^(x))f(y)dy

A function y=f(x) satisfies f''(x)=-(1)/(x^(2))-pi^(2)sin(pi x)f'(2)=pi+(1)/(2) and f(1)=0 then value of f((1)/(2)) is

A function y=f(x) satisfies f(x)=-(1)/(x^(2))-pi^(2)sin(pi x);f'(2)=pi+(1)/(2) and f(1)=0. The value of f((1)/(2))

A derivable function f(x) satisfies the relation f(x)=int_(0)^(1)xf(t)dt+int_(0)^(x)x^(2)f(t)dt. The value of (2f'(1))/(f(1)) is

Find the differentiable function which satisfies the equation f(x)=-int_(0)^(x)f(t)tan tdt+int_(0)^(x)tan(t-x)dt where x in(-(pi)/(2),(pi)/(2))