MATH138 Midterm: MATH138, lec 1 term test 1
15 Sep 2018
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Areas under curves, riemann sums, definite integrals. Intro to des, separable des, linear des, ivps. Overall goal find a way to determine the area under the graph of a function. Before we get into the theory, let us see how we could approximate the area. The easiest way is to break up the area into rectangles. (there are other ways: trapezoids, parabolas, etc. ) Also we can choose different points to calculate the height: left/right endpoints or midpoints. Say, we want to approximate the area under () from = to =. We can write down the formulas to get the area of all rectangles. Say, each rectangle is the same width and there are of them. Left endpoints: total area (0) +(1) + +( 1) . Midpoints: say 1,2, , are the midpoints, then the approximate is. Example: use 4 subintervals to approximate the area under () =2 + from = 2 to =
