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This is a problem from Tom Apostol's calculus book (the very first problem set in the introduction). It wants you to find
\(\displaystyle \int_0^b (ax^m+c)\,dx\)
using Archimedes' method of exhaustion. I'm attaching a diagram and a pdf of my work for the problem since it's rather involved.
I'm doing this rather mechanically since I don't have the intuition for it yet and so I'm wondering if anyone could point me in the right direction. (It's quite possible I'm making a silly error.) Thank you so much!
See the pdf below for the problem.
View attachment 1699
\(\displaystyle \int_0^b (ax^m+c)\,dx\)
using Archimedes' method of exhaustion. I'm attaching a diagram and a pdf of my work for the problem since it's rather involved.
I'm doing this rather mechanically since I don't have the intuition for it yet and so I'm wondering if anyone could point me in the right direction. (It's quite possible I'm making a silly error.) Thank you so much!
See the pdf below for the problem.
View attachment 1699
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