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



Integrate the following using the formula below: \( \int_{0}^{4} x^{2} \sqrt{16-x^{2}} d x \).| Define \( a, u \), and \( d u

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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the given integral is, ?04x216?x2dx=?04x242?x2dx
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