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Find the area of the region enclosed by one loop of the curve.

r = 7 cos 8{eq}\theta {/eq}

Question:

Find the area of the region enclosed by one loop of the curve.

r = 7 cos 8{eq}\theta {/eq}

Area Under Curves:

Area of the region enclosed by the curve is given by the definite integration. For a curve having farthest point from the origin is r, then the area enclosed by the curve is:

{eq}A = \frac{1}{2} \int r^2 d \theta {/eq}

Answer and Explanation: 1

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Here, we use some trigonometric formulas:

{eq}sin^2 \theta + cos^2 \theta = 1 \\ sin^2 \theta = \frac{1-cos2\theta}{2} {/eq}

One loop is created by...

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Evaluating Definite Integrals Using the Fundamental Theorem

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Chapter 16 / Lesson 2
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In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.


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