MAT 1332 Lecture Notes - Lecture 1: Partial Fraction Decomposition, Function Composition, 32X
9 Dec 2018
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This session covers sections 7. 3, 7. 4, and 7. 5 (with partial fraction). We divide the interval [0,1] into five subintervals of equal length. The mesh points are x0 = 0, x1 = 0. 2, x2 = 0. 4, x3 = 0. 6, x4 = 0. 8, x5. At the right end of each subinterval, x = 0. 2, 0. 4, 0. 6, 0. 8, and 1. Since the function f x e x is decreasing, the right sum. 5r is an underestimate of the actual area. Let the students to calculate an estimation of this integral with m5. The midpoints of subintervals are 0. 1, 0. 3, 0. 5, 0. 7, and 0. 9. Separate the integrand into the difference of two fractions: Points to emphasize: if the denominator is only a power of x, separate the fraction into a sum or difference of two fractions. This always makes the question easier: remember convert between the fractional/radical form and the negative/fractional exponent form if needed.
