You are here:

Calculus/double integral help

Advertisement

Expert: - 5/4/2010


Question
Use polar coordinates to calculate ∫∫R 1/((x^2 +y^2)^1/2)dA where R is the region inside the cardioid r = 1 + sin θ and above the x-axis.

I know r = ((x^2 +y^2)^1/2) making the equation ∫∫R 1/r drdθ but that's about as far as I've got! Is the upper limit for the inside ∫ '1 + sin θ'? Not sure about the lower limit though. Is it r=1?
And what will be the limits for the outside ∫?

Thanks a lot!

Answer
This is converted to polar coordinates by the function ∫∫ f(x,y) dx dy = ∫∫ r f(r,Θ) dr dΘ.
Note that there is an r in this conversion.

It seems like the limits would be for r to go from 0 to sinΘ, and then Θ to go from 0 to 2π.  

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.