Question

Integrate: x^2 sqr rot (4x^3 - 16)dx from 2 to 5

Answer 1

\[\int_2^5 x^2\sqrt{4x^3-16}~dx\]
Set \(u=4x^3-16\), so that \(du=12x^2~dx\), or \(\dfrac{du}{12}=x^2~dx\).
\[\frac{1}{12}\int_{16}^{484} \sqrt{u}~du\]