If `a >0,` find `int_0^(3a)|x^2-a^2|dxdot`

Explanation

I `=\int_{0}^{3 a}|x^{2}-a^{2}| d x \quad a>0 `


I `=\int_{0}^{a}(a^{2}-x^{2}) d x+\int_{a}^{3 a}(x^{2}-a^{2}) d x `


`=[a^{2} x-\frac{x^{3}}{3}]_{0}^{a}+[\frac{x^{3}}{3}-a^{2} x]_{a}^{3 a} `


`=[a^{3}-\frac{a^{3}}{3}]+[\frac{27 a^{3}}{3}-3 a^{3}-\frac{a^{3}}{3}+ a^{3}].`


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