Suppose that f is a continuous function on R and define a function F on [0, infinity) by f(x)= the integral of f from x to -x. Find a simple expression for F'(x).
Suppose that f is a continuous function on R and define a function F on [0, infinity) by f(x)= the integral of f from x to -x. Find a simple expression for F'(x).
So
Let us take a primitive of f: . By the Fundamental theorem of Integral Calculus we get that , so: