# Find f(x) using the fundamental theorem of calculus

Find $$f(x)$$ if $$\int_0^{f(x)}t^2dt=\pi \cos(\pi x)$$ So what I did is , using the fundamental theorem of calc. part 2 $$\int_0^{f(x)}t^2dt=\pi \cos(\pi x) \Leftrightarrow \frac{f(x)^3}{3}-0=\pi \cos(\pi x)$$ so then $$(3(\pi \cos(\pi x))^{1/3} = f(x)$$ is this correct?

• it seems correct to me – the_candyman May 20 at 20:12