3. Evaluate f S sin 0 dA, where R is the region in the first quadrant that is outside the circle r = 2 and inside the cardioid r = 2(1+ cos 0).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Need solution of 3 and 4
du
du
1. If u = Sin-1 V- Prove that x-
дх
2. Show that f(x, y) = e* sin y + e' cosx satisfy Laplace's equation + = 0.
3. Evaluate S S sin 0 dA, where R is the region in the first quadrant that is outside the circle r = 2
and inside the cardioid r = 2(1+ cos 0).
4. Show that the area of a region R enclosed by a simple closed curve C is given by
A =$(xdy – ydx) = $ xdy = - $ ydx, Hence, calculate the area of the ellipse x = a coso,
y = b sing (Green theorem)
Transcribed Image Text:du du 1. If u = Sin-1 V- Prove that x- дх 2. Show that f(x, y) = e* sin y + e' cosx satisfy Laplace's equation + = 0. 3. Evaluate S S sin 0 dA, where R is the region in the first quadrant that is outside the circle r = 2 and inside the cardioid r = 2(1+ cos 0). 4. Show that the area of a region R enclosed by a simple closed curve C is given by A =$(xdy – ydx) = $ xdy = - $ ydx, Hence, calculate the area of the ellipse x = a coso, y = b sing (Green theorem)
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