Chapter 9: Q. 31 (page 775)

Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by the function $r = a$ , where $a$ is a positive constant.

Short Answer

Expert verified

The area bounded by the function is $\frac{4 π^{3}}{6} {unit}^{2}$

Step by step solution

Given information

The function is $r = a$ , where $a$ is a positive integer.

Area

The area of the curve is given by,

$A = \frac{1}{2} \int_{α}^{β} r^{2} d θ A = \frac{1}{2} \int_{0}^{2 π} a^{2} d θ A = \frac{1}{2} {[\frac{a^{3}}{3}]}_{0}^{2 π} A = [\frac{{(2 π)}^{3}}{6} - 0] A = [\frac{8 π^{3}}{6}] A = \frac{4 π^{3}}{6} {unit}^{2}$

The area of the curve is $A = \frac{4 π^{3}}{6} {unit}^{2}$

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Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by the function $r = a$ , where $a$ is a positive constant.

Short Answer

Step by step solution

Given information

Area

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Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by the function r=a, where a is a positive constant.

Short Answer

Step by step solution

Given information

Area

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

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Pure Maths

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by the function $r = a$ , where $a$ is a positive constant.