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Polar Equations Calculus

Just because your equation is polar doesn't mean you can't do Calculus! Some tricks can extend the toolkit of Calculus to these special equations.

Polar Equations - Surface Area

         

Find the area of the surface formed by revolving the curve \(r = 5 \sin\theta\) from \(\theta = 0\) to \(\theta = \frac{\pi}{2}\) about the \(x\)-axis.

Find the surface area generated when the curve \( r = e^{\theta}\) from \(\theta = 0\) to \(\theta = \frac{\pi}{2}\) is revolved about the \(y\)-axis.

Find the area of the surface formed by revolving the curve \(r = 5 \sin\theta\) from \(\theta = 0\) to \(\theta = \frac{\pi}{2}\) about the \(y\)-axis.

Find the area of the surface formed by revolving the curve \(r = 3 \cos(\theta)\) from \(\theta = 0\) to \(\theta = \frac{\pi}{2}\) about the \(x\)-axis.

Find the area of the surface formed by revolving the curve \(r = 5 \cos{\theta}\) from \(\theta = 0\) to \(\theta = \frac{\pi}{2}\) about the \(y\)-axis.

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