MATH128 Study Guide - Quiz Guide: Improper Integral, Direct Comparison Test

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Behold the comparison test for type i improper integrals: Let f (x) and g(x) be continuous functions with f (x) g(x) 0 for x a. Then: if r , if r a f (x)dx is convergent then so is r a g(x)dx is divergent then so is r . Note that the test will only tell you whether or not an integral converges, it can"t help you nd the value of the improper integral if it does. a f (x)dx. a g(x)dx. In practice, you will be given one function in the problem and you will have to come up with the other one, and this can be hard. If the function is a quotient of two other functions involving polynomials, you can usually ignore all but the highest power of x in the top and bottom. For example, we would compare x2 + 3x + 9 x3 + 1 to x2 x3 =

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