Specialist2023 Exam 2 Section A · Q11CAS active1 mark

Surface area of revolution about the y-axis

The area of the curved surface generated by revolving part of the curve with equation $y = \cos^{-1}(x)$ from $\left(0, \frac{\pi}{2}\right)$ to $(1, 0)$ about the $y$ -axis can be found by evaluating

1 mark

2\pi \int_{0}^{\frac{\pi}{2}} \left(\cos^{-1}(x)\sqrt{1 + \frac{1}{x^2 - 1}}\right) dx

2\pi \int_{0}^{1} \left(\cos^{-1}(x)\sqrt{1 + \frac{1}{x^2 - 1}}\right) dx

2\pi \int_{0}^{\frac{\pi}{2}} \cos(y)\sqrt{1 - \sin^2(y)}\, dy

2\pi \int_{0}^{\frac{\pi}{2}} \sqrt{1 + u^2}\, du

, where

u = \sin(y)

2\pi \int_{0}^{1} \sqrt{1 + u^2}\, du

, where

u = \sin (y)

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