Find $\int \cos^2 (3x)\,\mathrm{d}x$.[2] Find $\int \frac{1-x}{\sqrt{2-x^2}}\,\mathrm{d}x$.[3] T

Question

Find $\int \cos^2 (3x)\,\mathrm{d}x$.[2] Find $\int \frac{1-x}{\sqrt{2-x^2}}\,\mathrm{d}x$.[3] The region bounded by the curve $y = 2\sin x$, the line $y = 3 - 2x$ and the $y$-axis is rotated through $2\pi$ radians about the $y$-axis. Find the volume of the solid obtained, leaving your answer correct to 3 decimal places.[6]

Accepted Answer

(a) $\dfrac{x}{2}+\dfrac{\sin6x}{12}+C$ (b) $\sin^{-1}\!\left(\dfrac{x}{\sqrt2}\right)+\sqrt{2-x^2}+C$ (c) $1.878\text{ units}^3$

2024 MI PRU2 P1 Q9

2024 MI PRU2 P1 Q9

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