A- z1 /(S+ 10cosede TT

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question

Inner loop of r=5+10cos(Θ)

find the area of the given region 

I set it up as A=2(1/2)intgral ((5+10cos(Θ))^2)dΘ 

b=pi

a=2pi/3

can you help me find the area

A- z1
/(S+ 10cosede
TT
Transcribed Image Text:A- z1 /(S+ 10cosede TT
Expert Solution
Step 1

Use the area formula of polar graphs. Area= (1/2)*integration r^2 dtheta from 2pi/3 to pi.

Area
(5+10cos0'd
2T
(25+100cos0+100 cos'0 )d0
2
2T
3
Step 2

Simplify the integrals then plug the limits.

- 502 cos'0 d0
[250+100sinø]2 + }
2
3
2
3
2T
+100sin
3
2л
25л+100sinл-(25.
2
+25(cos20+1)d0
3
3
507
-+50 V3+25
1
25T-
2
sin20
+0
2
2T
3
2л
sin2
25T
sin27
-503+25
3
+
3
2
2
2
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