Please help. This is a double integral problem. Thank you. Sketch the region and use a double integral to find its area.The region bounded by the cardioid r= - 3(1 - sin 0)

Name: Please help. This is a double integral problem. Thank you. Sketch the
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Description: Please help. This is a double integral problem. Thank you. Sketch the region and use a double integral to find its area.The region bounded by the cardioid r= - 3(1 - sin 0)

The cardioid is r=-31-sinθ, θ r=-31-sinθ 0 r=-3 π6 r=-32 π4 r=-31-12 π3 r=-31-32 π2 r=0…

Answered: Sketch the region and use a double…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please help. This is a double integral problem. Thank you.

Sketch the region and use a double integral to find its area.
The region bounded by the cardioid r= - 3(1 - sin 0)

Expert Solution

Solution:

The cardioid is $r = - 3 (1 - \sin θ)$ ,

$θ$	$r = - 3 (1 - \sin θ)$
0	$r = - 3$
$\frac{π}{6}$	$r = - \frac{3}{2}$
$\frac{π}{4}$	$r = - 3 (1 - \frac{1}{\sqrt{2}})$
$\frac{π}{3}$	$r = - 3 (1 - \frac{\sqrt{3}}{2})$
$\frac{π}{2}$	$r = 0$

The graph begins in third quadrant and ends up in second quadrant at $r = - 3$ .

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