Let f(x)=integral(-1 to x) sqrt(1-t^2) dt for all x E |-1,1|

(1)Use fundamental theorem of calculus to evaluate F'(x) for all x |-1,1|

(2)explain why f(x) is invertiable on |-1,1|

(3)Let G(y) denote inverse of F(x).state domain and range of g(y) and evaluate G(pi/4)

(4)evaluate G'(pi/4)

(Hint:use inverse function theorem to express the derivative ofG(y) in terms of derivative of F(x)

For diagram please see the attach