Question
Asked Dec 4, 2019
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Find the area of the cardioid r = 4 + 3 sin theta that lies in Quadrants I and IV.

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Expert Answer

Step 1

Given the cardioid that lies in the 1st and 4th quadrant

r = 4+3 sin e
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r = 4+3 sin e

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Step 2

Make the sketch of the cardioid and write the formula of the area

T-4+3 sin e
Area A = |
de
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T-4+3 sin e Area A = | de

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Step 3

Plug the limits and find the area of the cardioid which is...

de
Area A =
4+3sin 6) de
(16+9 sin e+24 sin e) de
(1-cos 20
16+9
+24 sin e
Пgo
cos 20+12 sin
4 4
41
9
-cos 20 +12 sin e
4
41 9
-cos 20+12 sin 0
4
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de Area A = 4+3sin 6) de (16+9 sin e+24 sin e) de (1-cos 20 16+9 +24 sin e Пgo cos 20+12 sin 4 4 41 9 -cos 20 +12 sin e 4 41 9 -cos 20+12 sin 0 4

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Tagged in

Math

Calculus