AM-1973

Area below the x-axis

A Math · Secondary 4 · Hard · Area below the x-axis

The curve

y = 3\cos x - 1

intersects the x-axis at points C and D, where C has the smaller positive x-coordinate. Find the exact area of the region bounded by the curve and the x-axis between C and D.

$2\pi-2\cos^{-1}\!\left(\tfrac13\right)+4\sqrt{2}$
$2\cos^{-1}\!\left(\tfrac13\right)$
$\pi-2\cos^{-1}\!\left(\tfrac13\right)$
$2\pi+2\cos^{-1}\!\left(\tfrac13\right)$

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