# A little bit of both

Calculus Level 5

For which real numbers $$a$$ and $$b$$ with $$0\leq{a}\leq{b}\leq{1}$$ is $\int_{a}^{b}\left(\cos(7\pi{x})-\cos(9\pi{x})\right) \ dx$ maximal? Find $$A=a\times b$$.

No calculators, please; they spoil all the fun.

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