Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be the function satisfying `f(x)+g(x)=x^(2)`.Prove that,
`int_(0)^(1)f(x)g(x)dx=(1)/(2)(2e-e^(2)-3)`

Let f(x)be a function satisfying f(x)=f(x) with f(0)=1 and 'g' be the function satisfying f(x)=g(x)=x^2 the value of the integral int_0^1f(x)g(x)dx is

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satisfies f(x)+g(x)=x^(2) . Then the value of the integral int_(0)^(1) f(x)g(x) dx is equal to -

f(x)=e^x.g(x) , g(0)=2 and g'(0)=1 then f'(0)=

Let f:R ->(0,oo) be a real valued function satisfying int_0^x tf(x-t) dt =e^(2x)-1 then find f(x) ?

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , then evaluate int_(sintheta)^(cos e ctheta)f(x)dx

Let f(x)=(1)/(1+x^(2)) and g(x) is the inverse of f(x) ,then find g(x)

Let f(x) = x + cos x + 2 and g(x) be the inverse function of f(x), then g'(3) equals _

Let f(x)=x^(2) and g(x)=2x+1 be two real functions. Find (f+g) (x), (f-g) (x), (fg) (x), (f/g) (x) .