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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?

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    $\begingroup$ it seems correct to me $\endgroup$ – the_candyman May 20 at 20:12

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