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(Solved): 1. Integrate the following using the formula below: \( \int_{0}^{4} x^{2} \sqrt{16-x^{2}} d x \). D ...




1. Integrate the following using the formula below: \( \int_{0}^{4} x^{2} \sqrt{16-x^{2}} d x \). Define \( a, u \), and \( d
1. Integrate the following using the formula below: \( \int_{0}^{4} x^{2} \sqrt{16-x^{2}} d x \). Define \( a, u \), and \( d u \) as part of your work. ( 9 pts.) \[ \int u^{2} \sqrt{a^{2}-u^{2}} d u=\frac{u}{8}\left(2 u^{2}-a^{2}\right) \sqrt{a^{2}-u^{2}}+\frac{a^{4}}{8} \sin ^{-1}\left(\frac{u}{a}\right)+C \]


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