MATH 1007 Lecture Notes - Lecture 13: 32X, The Thirteen Chairs
6 Apr 2016
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If f is non negaive (all above x-axis) and coninuous on [a,b], then integral a to b of f(x)dx is equal to the area of the region under the graph of f on [a,b] Suppose f is coninuous on [a,b]: two parts:::: If g(x) = integral a to x f(t)dt. Then, g"(x) = f(x) for all x in [a,b] ** the integraion is from some nuber to a variable. Integral a to b of f(x)dx = f(b) - f(a) Where f is any aniderivaive of f, that f"=f. The purpose of all this is to right away ind the derivaive of an integral funcion without having to ind g(x) irst!!! When you have a funcion instead of x in the upper limit, then you replace it by u to make it easier, do the whole thing, then sub in the value of u at the end! If g(x) = integral a to x of cos(t)dt, then g"(x) = cosx.
