Find $\displaystyle\int{x{{\left( \ln x \right)}^{2}}\mathrm{ d}x}$. [4] The region $R$ is bounded b

Question

Find $\displaystyle\int{x{{\left( \ln x ight)}^{2}}\mathrm{ d}x}$. [4] The region $R$ is bounded by the curves $y=	an x$, $y=\cos 2x$ and the $y$-axis. Find the numerical value of the volume of the solid obtained when $R$ is rotated through $2\pi $ radians about the $y$-axis. [3]

Accepted Answer

$\dfrac{x^{2}}{2}(\ln x)^{2}-\dfrac{x^{2}}{2}\ln x+\dfrac{x^{2}}{4}+C$ (b) $0.324$ units³

2019 YIJC Promo Q4

2019 YIJC Promo Q4

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