- #1
salman213
- 302
- 1
1. The question was find the area between the curves using DOUBLE Integrals
Area between:
r = sin theta
r = cos theta
well to draw them i made them into cartesian form by
r^2 = rsin theta
r^2 = rcos theta
so
x^2 + y^2 = y
x^2 + y^2 = x
completing square
1) x^2 + (y - 1/2)^2 = 1/4
2) (x - 1/2)^2 + y^2 = 1/4
these are two circles
their intersection or bounded region that we need to find the area is like a disc...
I know if i use the double integral
Integral of (Integral of 1) dA OVER D where D is the intersection bounded area
i get the area i need...
but I don't know how to define that region
if someone can help me define the region it will be helpful
I know THETA will change from 0 to pi/2
but R will change from 0 to some equation of that area but i don't know how to find that equation!
HELP!
Area between:
r = sin theta
r = cos theta
well to draw them i made them into cartesian form by
r^2 = rsin theta
r^2 = rcos theta
so
x^2 + y^2 = y
x^2 + y^2 = x
completing square
1) x^2 + (y - 1/2)^2 = 1/4
2) (x - 1/2)^2 + y^2 = 1/4
these are two circles
their intersection or bounded region that we need to find the area is like a disc...
I know if i use the double integral
Integral of (Integral of 1) dA OVER D where D is the intersection bounded area
i get the area i need...
but I don't know how to define that region
if someone can help me define the region it will be helpful
I know THETA will change from 0 to pi/2
but R will change from 0 to some equation of that area but i don't know how to find that equation!
HELP!