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Integration Challenge

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,642
Find all continuous functions $f:[1,\,8] \rightarrow \mathbb{R} $ such that

$\displaystyle \int_1^2 f^2(t^3)dt + 2\int_1^2 f(t^3)dt=\dfrac{2}{3}\int_1^8 f(t)dt-\int_1^2 (t^2-1)^2 dt$