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Gerard Sayson TMUA Mock Paper 1 · Q9

Paper 1CalculusGeometryPowers & logarithms

The region RR is bounded by the curves y=2ln⁡xxy=\dfrac{\sqrt{2\ln x}}{x} and y=ln⁡xxy=\dfrac{\ln x}{x}.

The formula

V=∫abπ[f(x)]2 dxV=\int_a^b\pi[f(x)]^2\,\mathrm{d}x

can be used to find the volume generated by rotating the area under the curve from x=ax=a to x=bx=b about the xx-axis. Determine the exact volume generated by rotating RR about the xx-axis through 2π2\pi radians.

A2π−10πe−22\pi-10\pi e^{-2}
B4πe−2−π4\pi e^{-2}-\pi
C4πe−24\pi e^{-2}
D4πe−44\pi e^{-4}

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