iterated double integral: int int [sqrt(25-x^2-y^2)] dy dx

[epicjr77]

Below I have a very complex problem. I understand that I first have to intergate the inside with respect to dy, and then integrate the outside with respect to dx. My problem is that I have looked around in my text book, Calculus, by Swokowski, and I can't seem to find how to intergrate this square root. I also don't understand how to solve the problem. Here it is:

The iterated double integral represents the volume of a solid under a surface S and over a region R in the xy plane. Describe S

. . .int[0, 1] int[3-x, 3-x^2] [sqrt(25 - x^2 - y^2)] dy dx

Thank you for any help!

 

[mammothrob]

Well, it just so happens that I studied from that same book, looking at 17.2 right now actually. If you are only trying to complete the objective the book is giving , all you need to do it draw the region and write out the equations that describe it.

Heres how to start it.

Look at the dy part and its limits. y goes from 3-x to 3-(x^2).

so y=3-x and y=3-x^(2) what do those graps look like?... I bet your graphing them out right now.

If you solve for the intersections, the dx part should start to make sense.

If you want to do well in the following sections you need to get this stuff on lock down... after you see whats going on here you should try to re-write the limits so it's dxdy.

Rob