I'm studying for my final and tutors/my professor isn't available over the weekend. Could someone please spend a little time to help me? My problem is stated as:(adsbygoogle = window.adsbygoogle || []).push({});

Let R be the right half of the circle x^{2}+(y-1)^{2}=1. Use a double integral polar coordinates to find the area of the region R.

I could solve for this easily if the circle wasn't shifted up 1, could someone tell me what I should do in order to solve this problem?

Some of my guesses:

I think it should still be taken in the region 3∏/2 to ∏/2 as my outside integral (right half of the circle). I could be wrong, would adding 1 to those values fix it?

I don't know how to express r (radius) in my inside integral (unless it's still going to be 0 to 1). My professor attached the note of "You will need to convert the given circle into polar form."

Doing this, I got:

R=x^{2}+(y-1)^{2}=1

R=r^{2}cos^{2}θ+(rsinθ-1)^{2}=1

R=r^{2}cos^{2}θ+r^{2}sin^{2}θ-2rsinθ+1=1

R=r^{2}-2rsin+1=1

I'm not sure if I'm doing this right, but what's after that?

Any help is appreciated, please let me know if you require any additional information or if I'm making something unclear.

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# Homework Help: Double Integral Polar Coordinates to find area of region

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