MTH 252H Midterm: MTH 252H - Term Test 1
15 Sep 2018
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The slope of the line tangent to the graph of the position function at a certain time gives the velocity at that time. The inverse of this can give us the position function if we take the integration of the velocity. The strategy is to divide the time interval into many subintervals and approximate the velocity on each subinterval by a constant velocity. Then the displacements on each subinterval are calculate and summed. Sigma (or summation) notation is used to express sums in a compact way. The symbol (sigma, the greek capital s) stands for sum. Slice-and-sum method: slicing a region into smaller parts, summing the results from the parts, and taking a limit is called slice-and-sum method. If u is any differentiable function of x, then n u du. Substitute u = g(x), du = g"(x)dx, and integrate with respect to u from u = g(a) to u = g(b) b a xgf dxxg bg ag duuf.
