13.4 Polar Coordinates

13.4 Polar Coordinates - 
 1 3.4 
P o l a r 
C o o r...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 
 1 3 .4 
P o l a r 
C o o r d in a t e s 
 
 x = r cosθ y = r sin θ y tan θ = x
 


























 x 2 + y 2 = r2 
 
 
 
 
 
 
 
 
 
 
 
 ∫∫ f ( x, y ) dA = ∫ β α R ∫ b a f ( r cos θ, r sin θ ) r drdθ α ≤ θ ≤ β and a ≤ r ≤ b .
 
 Ex.

Let
R
be
the
region
shown
below.
 3 2 1 -3 -2 -1 1 2 3 -1 -2 
 -3 
 
 
 
 Ex.
 2 1 -2 -1 1 2 -1 -2 
 
 

where
 
 
 
 
 
 
 
 
 
 1 ∫∫ 1− x 2 1 − x 2 − y 2 dydx 
by
 Ex.

Evaluate
 0 0 changing
to
polar
coordinates.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 ∫∫ 2− x dydx Ex.
Set
up
an
integral
to
evaluate
 0 x 
by
changing
 to
polar
coordinates.
 
 
 
 
 
 
 
 
 
 
 Ex.
Find
the
area
inside
 r = 4 cosθ 
and
outside
r
=
2.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Do:
Set
up
an
integral
to
evaluate
 0 ∫∫ −2 0 4 −y 2 x 2 + y 2 dxdy 
by
changing
to
polar
 coordinates.
 
 

 
 
 
 
 
 
 
 ...
View Full Document

This note was uploaded on 10/02/2011 for the course AERO 1234 at Virginia Tech.

Ask a homework question - tutors are online