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Q. 17

Expert-verified

Calculus

Found in: Page 756

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Find a definite integral expression that represents the area of the given region in the polar plane and then find the exact value of expression
The region bounded enclosed by the spiral $r = θ$ and the x-axis on the interval $0 \leq θ \leq π$

The integral can be given as $\frac{1}{2} \int_{0}^{π} θ^{2} d θ$ . The exact value of integral can be given as 5.165 units

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

We are given an equation of spiral as $r = θ$

Step 2: Evaluate

The area can be given as

$A = \frac{1}{2} \int_{0}^{π} r^{2} d θ A = \frac{1}{2} \int_{0}^{π} θ^{2} d θ A = \frac{1}{2} (10.33) A = 5.165 u n i t$

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