MAT 211 Quiz: Chapter 7 Study Guide Notes
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Provide a generalization to each of the key terms listed in this section. [f (x i ) g (x i )] x. 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 0 i=1 a (x) xi (cid:80)n. 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. A = lw lw dx = lwh (cid:90) h. The previous formula pretty much occurs when you have all of x being thick. When it comes to cross-sections of an area, which would be a(x) in this case, while it"s perpen- dicular to the x-axis, then the following would be the proper volume: y-axis.
