Evaluate $\displaystyle\int\nolimits_{1}^{4}{\left| {{a}^{2}}-{{x}^{2}} \right|}\,\mathrm{d}x$ whe

Question

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

Accepted Answer

$\frac{4}{3}{{a}^{3}}-5{{a}^{2}}+\frac{65}{3}$

Applications of Intergration