<ol class="abc-list"><li><div class="list-item-paragraph">Find \(\int \cos^2 (3x)\,\mathrm{d}x\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Find \(\int \frac{1-x}{\sqrt{2-x^2}}\,\mathrm{d}x\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">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.<span class="inline-marks">[6]</span></div></li></ol>

Find \(\int \frac{1-x}{\sqrt{2-x^2}}\,\mathrm{d}x\).

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.

2024 MI PRU2 P1 Q9

2024 MI PRU2 P1 Q9