MATH 111 Lecture 24: Integrals Part5
13 Jul 2015
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The substitution rule for indefinite integrals (continuation from lecture 23) The substitution rule for definite integrals (continuation from lecture 23) If g" is continuous on [a,b] and f is continuous on the range of u=g(x), then: **with indefinite integrals, the u-substitution needs to be undone after the function is evaluated. With definite integrals (since a value is the answer, not a function), the function can be evaluated as a function of u, not x. If a function is even (eg. y=x2), a f(x)dx. If a function is odd (eg. y= x3) a f(x)dx = 2 0.
