MTH 161 Study Guide - Quiz Guide: Riemann Integral, Hypotenuse, Ds 4
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Provide a generalization to each of the key terms listed in this section. [f (x i ) g (x i )] x. [f (x) g (x)] dx =z b a. 1 perpendicular to the x-axis with a(x) being any integrable function, then the formula for a solid"s volume would be the following: V = limmax xi 0pn i=1 a (x) xi a a (x) dx. The previous integral is actually constant for every cross-section. If you have every cross-section with x thickness while each having some height to them, then just add several r2 x"s, which will make it sound like it"s a riemann integral. The previous formula pretty much occurs when you have all of x being thick. If you let f be a function that on the closed interval of [a, b], then the following existing limit would be f "s de nite integral while it"s from from a to b:
