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13 Nov 2019
1. Let R be the region above the x-axis and under the curve y = f(x)-11-3x2 on the interval [0,1]. We want to calculate the area of region R with a definite integral. Sketch region R and express its area as a definite integral. Do not evaluate. a) Suppose the area of region R is approximated with n equal-width rectangles. Derive an expression for Ar, the width of each rectangle, in terms of n. b) Find an expression for the right endpoint of the i-th subinterval. Then find an expression for the height of the i-th rectangle at the right endpoint of the i-th subinterval. The expression should be in terms of i and n. c) Find an expression for the area of the i-th rectangle in terms of i and n.
1. Let R be the region above the x-axis and under the curve y = f(x)-11-3x2 on the interval [0,1]. We want to calculate the area of region R with a definite integral. Sketch region R and express its area as a definite integral. Do not evaluate. a) Suppose the area of region R is approximated with n equal-width rectangles. Derive an expression for Ar, the width of each rectangle, in terms of n. b) Find an expression for the right endpoint of the i-th subinterval. Then find an expression for the height of the i-th rectangle at the right endpoint of the i-th subinterval. The expression should be in terms of i and n. c) Find an expression for the area of the i-th rectangle in terms of i and n.
Trinidad TremblayLv2
8 Jan 2019