I am currently taking calculus 3 and I am a little confused about the concept of double and triple integrals. Analytically, it's a breeze. I understand how to set limits, do all calculations, etc.(adsbygoogle = window.adsbygoogle || []).push({});

What my question is, when I get an answer, what does the answer "mean"? For example, in this problem:

whereEis the solid bounded by and the plane

[FONT=Times New Roman, serif]Correct me if I'm wrong here, but I'll try to explain the way I understand. [/FONT]

and y = 8 is the shape of the region that I'm integrating over. Lets say dV= dxdydz. Even if we removed the function under the integral, the shape of the region would remain the same. So what does the function represent geometrically? If we drop the function from the integral, we are left with the volume of the region described in the limits, correct? So what does the function tell us? And after integration, what does the result tell us?

Im really looking for a real world application of this stuff so I understand what exactly I am doing. Maybe in physics? When I asked my teacher, "what does the answer tell us/mean?" she responded "its the answer to the integral." Didn't really help.

Any help would be great. I am happy to be corrected! :)

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# Geometric interpretations of double/triple integrals

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