Let `f(x) = x^3 + x-2` be a function than ` int_ -2^0 g(x)dx` equals where `g(x)=f^(-1)x`

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

Let f,g, h be 3 functions such that f(x)gt0 and g(x)gt0, AA x in R where int f(x)*g(x)dx=(x^(4))/(4)+C and int(f(x))/(g(x))dx=int(g(x))/(h(x))dx=ln|x|+C . On the basis of above information answer the following questions: int f(x)*g(x)*h(x)dx is equal to

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

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

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

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 :

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_0^1f(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_0^1f(x) g(x) dx , is

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be 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)