Area with Trigonometric Curves

Find the area between curves where at least one involves trigonometric functions (sin, cos), often requiring trigonometric integration.

2 questions · Challenging +1.0

1.08f Area between two curves: using integration

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CAIE P2 2022 June Q7

8 marks Standard +0.8

7 \includegraphics[max width=\textwidth, alt={}, center]{1b9c6b41-69dd-4132-92c7-9507cbd741dd-10_551_657_274_735} The diagram shows the curves \(y = \sqrt { 2 \pi - 2 x }\) and \(y = \sin ^ { 2 } x\) for \(0 \leqslant x \leqslant \pi\). The shaded region is bounded by the two curves and the line \(x = 0\). Find the exact area of the shaded region.

CAIE P2 2022 June Q7

8 marks Challenging +1.2

7 \includegraphics[max width=\textwidth, alt={}, center]{712be8e6-e1e9-4662-b1f1-51c39c2c9df1-10_551_657_274_735} The diagram shows the curves \(y = \sqrt { 2 \pi - 2 x }\) and \(y = \sin ^ { 2 } x\) for \(0 \leqslant x \leqslant \pi\). The shaded region is bounded by the two curves and the line \(x = 0\). Find the exact area of the shaded region.