Please help:( I tried every method possible but still can't figure out. Calc 3 btw
Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=5 and between the circles x^2+y^2=100 and x^2−10x+y^2=0.

Question

Please help:( I tried every method possible but still can't figure out. Calc 3 btw
Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=5 and between the circles x^2+y^2=100 and x^2−10x+y^2=0.

zepdrix · Answer

|dw:1393632010453:dw|So we've got something like this, yes?

zepdrix · Answer

|dw:1393632053197:dw|And we want to find the area of this region.

zepdrix · Answer

hmm

zepdrix · Answer

Before we write this in polar, try to think logically a sec.
Our angle will span from $\Large\bf\sf \theta \in [0, \pi/2]$

Does that make sense?
Our angle traces out the whole first quadrant.

zepdrix · Answer

Ohh below the line y=5 woops!
I forgot something in the drawing! :)

zepdrix · Answer

|dw:1393632224727:dw|

zepdrix · Answer

Sooo ok I take that back.
Our angle is going to be a little trickier.|dw:1393632382523:dw|