Rotation In Maths II

Calculus Level 4

The volume of the solid generated by the revolution about the initial line of the area bounded by the curve r = f ( θ ) r = f(\theta) and the radii vectors θ = α \theta = \alpha and θ = β \theta = \beta is given by:

This Problem Is A Part Of Rotation In Maths .
2 π 3 ∫ β α r sin ⁡ θ d θ \displaystyle \dfrac{2\pi}{3} \int_{\beta}^{\alpha}r\sin\theta \mathrm{d}\theta 2 π 3 ∫ β α r 3 sin ⁡ 3 θ d θ \displaystyle \dfrac{2\pi}{3} \int_{\beta}^{\alpha}r^{3}\sin^3\theta \mathrm{d}\theta 2 π 3 ∫ β α r 3 sin ⁡ θ d θ \displaystyle \dfrac{2\pi}{3} \int_{\beta}^{\alpha}r^{3}\sin\theta \mathrm{d}\theta 2 π ∫ β α r 3 sin ⁡ 3 θ d θ \displaystyle {2\pi} \int_{\beta}^{\alpha}r^{3}\sin^3\theta \mathrm{d}\theta

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Vraj Mehta by Vraj Mehta , 30, India

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1 solution

Tom Engelsman
Mar 21, 2020

Just by converting from rectangular to polar coordinates:

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