Applications of Integration

Applications of Integration

Evaluate \(\displaystyle\int_{1}^{4}{\left| {{a}^{2}}-{{x}^{2}} \right|}\,\mathrm{d}x\) where \(1<a<4\), giving your answer in terms of \(a\).

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Answer:\(\dfrac43a^3-5a^2+\dfrac{65}{3}\)

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