Consider the curves and on the interval .

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the curves y=cos⁡xy=\cos x and y=cos⁡2xy=\cos^{2}x on the interval x∈[0, π/2]x\in[0,\,\pi/2]. (i) Establish which curve provides the upper boundary and which provides the lower boundary on the stated interval. (ii) Hence evaluate the exact area of the region enclosed between the two curves for x∈[0,π/2]x\in[0,\pi/2]. Express your answer in simplest form.

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