MATH 182A Lecture Notes - Lecture 4: Improper Integral, 32X, 4Dx
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This is a proper integral. function y = x from 0 to 1. It represents the area under the curve of the. This is an example of an improper integral. It has no proper meaning because you cannot take the area under the curve from 0 to . The problem is only as hard as is the integration of f (x). We can rewrite it as: b z b lim a f (x)dx. Z b z b b z b lim lim. Let : f (x) = x 3/2dx g(x) = x 2 f (x) = 2. X g (x) = dx f (g(x)) = z (x 2) 3/2dx = . Let : t = 1 + x3 dt = 3x2dx. Evaluate using the original limits: b (cid:20) 1 + x3(cid:21)b lim. Evaluate using the original limits: b (cid:20) (ln(x))2 lim. 9 + x6 dx + z x2. 9+x6 is an even function, we can rewrite this as:
