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Q3. Find the area of the region R that lies outside the cardioid r = and inside the circle r a(1+ cos 0) 3a cos 0, where a > 0.

Q3. Find the area of the region R that lies outside the cardioid r = and inside the circle r a(1+ cos 0) 3a cos 0, where a > 0.

Advanced Engineering Mathematics
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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Q3. Find the area of the region R that lies outside the cardioid r = a(1 + cos 0) and inside the circle r 3a cos 0, where a > 0. Now assume that R denotes a thin plate of constant density p = 1. Write down the mass M of the plate, derive the formula |T/3 /3 cos" 0 do = 1 cos"-10 sin 0 (T/3 cos"-2 0 de, n E Z>2, n - 1 and use it in order to find the coordinates of the centre of mass (a, ) of the thin plate R.
Transcribed Image Text:Q3. Find the area of the region R that lies outside the cardioid r = a(1 + cos 0) and inside the circle r 3a cos 0, where a > 0. Now assume that R denotes a thin plate of constant density p = 1. Write down the mass M of the plate, derive the formula |T/3 /3 cos" 0 do = 1 cos"-10 sin 0 (T/3 cos"-2 0 de, n E Z>2, n - 1 and use it in order to find the coordinates of the centre of mass (a, ) of the thin plate R.
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