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# Answer to Question #3041 in Calculus for Keira Tachibana

Question #3041
Let R be the region in the first quadrant below the graph of y = cosx and above the graph of y = 2x.
a) Find the area of R.
b) Find the volume of the solid formed when R is revolved around the x-axis.
c) Find the volume of the solid formed when R is revolved around the line x = -1.
$cosx = 2x \\ x \approx 0.45 \\ S = \int_0^{0.45}(\cos{x} - 2x)dx = (-\sin x -x^2)_0^{0.45} = \\ = - \sin 0.45 - 0.45^2 \approx 0.43 - 0.20 = 0.23 \\ \\ V = \int_0^{2\pi}Sd\theta = 2 \pi S \approx 1.45 \\$

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