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Setup an integral that represents the area of the surface obtained by rotating the given curve...

Question:

Setup an integral that represents the area of the surface obtained by rotating the given curve about the y-axis. Then find the surface area.

{eq}x = 5 \cos \theta;\ \ \ \ 0 \leq \theta \leq \frac{\pi}{2}{/eq} and {eq}y = 5 \sin \theta{/eq}

Setting and Finding the Surface Area:

The objective is to setup an integral to find the surface area by using the given curves.

The general form of surface area about {eq}y {/eq} axis is {eq}\displaystyle Surface Area = \int_{a}^{b} 2 \pi x \ ds {/eq}

First, we have to find {eq}ds {/eq} and apply in general form.

By using the given limit, we have to integrate and get a solution.

Answer and Explanation: 1

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The given curves are:

{eq}x = 5 \cos \theta \\ y = 5 \sin \theta {/eq}

The given limit is:

{eq}0 \leq \theta \leq \frac{\pi}{2} {/eq}

To find...

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Evaluating Definite Integrals Using the Fundamental Theorem

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Chapter 16 / Lesson 2
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The fundamental theorem of calculus makes finding your definite integral almost a piece of cake. See how the definite integral becomes a subtraction problem after applying the fundamental theorem of calculus.


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