MATH 1A Lecture 23: MATH 1A - Lecture 23 - 5.1 Areas and Distances.docx
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Math 1a - lecture 23 - 5. 1 areas and distances. Q: find the area under the graph of y=f (x) from x=a to x=b . Area a=? (this is hard for general f ( x) at the moment, so we will do a simpler problem. ) This time y=c , where c is a constant. The area a is simple equal to height width=c (b a) So we can approximate the area of the first problem using a rectangle. Here we have drawn a rectangle with a height that reaches the local max of interval. f ( x ) in the. We can improve the approximation by using two rectangles. So we could get an arbitrarily close approximation to the actual area by using a larger number of rectangles. Suppose we have the function f ( x)=1 x2. Find the area under the curve between x=0 and x=1 . Suppose we want to use one rectangle to approximate:
