Find $\displaystyle\int{\frac{x+1}{4+3{{x}^{2}}}\mathrm{d}x}$. [4] The region bounded by the curve $

Question

Find $\displaystyle\int{\frac{x+1}{4+3{{x}^{2}}}\mathrm{d}x}$. [4] The region bounded by the curve ${{\left( y-1 \right)}^{2}}=x$ and the line $x=1$ is rotated through $2\pi $ radians about the $x$-axis. Find the volume of the solid obtained, giving your answer correct to $4$ decimal places. [3]

Accepted Answer

(a) $\frac{1}{6}\ln|4+3x^2| + \frac{\sqrt{3}}{6}\tan^{-1}\left(\frac{\sqrt{3}x}{2}\right) + C$, (b) $\frac{8\pi}{3} = 8.3776$ units³

2022 NJC Promo Q4

2022 NJC Promo Q4

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