Hi,

I don't understand how the limits in the solution of part (b) have been obtained. Please explain how it's done.

Thanks

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- June 1st 2009, 05:03 PMalgorithmDouble Integral Limits
Hi,

I don't understand how the limits in the solution of part (b) have been obtained. Please explain how it's done.

Thanks - June 1st 2009, 05:14 PMJester
- June 1st 2009, 05:47 PMDanneedshelp
Well, the limits from the first integral are given by the line and the section of the circle equation given by .

First, we can see that the first (inner) most integral is with respect to ; thus, we must solve our two equations for . Also, notice the second integral is with respect to . Therefore, we must make sure we only have y's in our second integrand. Solving our two equations for will give us that.

So, solving for we get and .

Therefore, we have as our inside integral. The limits are ordered the way they are, because the circle is above the line.

The outside integral just tells us how far up the y-axis to integrate. So, that’s where the limits are coming from.

And, just a note, when you are dealing with iterated integrals, always make sure your outer most limits are numbers and not functions.