using polar coordinates to find area

[Erin0702]

2a. Use polar coordinates to find the area of the region bounded by the two circles x²+y²=1 and x²+y²=4

2b.Then find the same area by elementary geometry to check your integration.



When converting to polar coordinates
r=x+y
so r²=x²+y²
Then I would have r²=4 and r²=1 which would give me r=±2 and r=±1.

From here I'm not sure where to go with it. Any help is greatly appreciated!

 

[stapel]

When converting to polar coordinates, r=x+y....

No. The hypotenuse is not the sum of the two legs.

...so r²=x²+y²

This statement is correct, but does not follow from the previous (incorrect) statement, since (x + y)² = x² + 2xy + y², which is not the same as x² + y² = r².

Just use the radii, and find the area, integrating in polar coordinates, between r² = 4 and r² = 1.

Eliz.

 

[Erin0702]

My book says that x²+y²=r² and since I'm given the equations x²+y²=4 and x²+y²=1 I thought I could make them r²=±2 and r²=±1?

 

[ChaoticLlama]

My book says that x²+y²=r² and since I'm given the equations x²+y²=4 and x²+y²=1 I thought I could make them r²=±2 and r²=±1?

It is critical to review algebra before studying calculus. Please see your teacher for extra help. The specific problems you are having with this question are not calculus related.

 

[Erin0702]

My problem isn't algebra...I'm converting the cartesian coordinates to polar coordinates. There is no algebra involved in that it simply says that x^2+y^2=r^2 everytime. I just made the mistake of also saying that r=x+y. All I needed to know was if I was going about solving this problem in the right way, I wasn't trying to perform any algebraic steps.

 

[stapel]

My problem isn't algebra.

According to what you have posted, you have somehow come to the conclusion that radii can be negative. This is a non-calculus difficulty that needs to be ironed out before proceeding.

Please take the tutor's advice to heart; it was meant to help you.

Thank you.

Eliz.