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MATH 101 HOMEWORK 7 Due on Wednesday Nov. 10, 2004. For full credit, show all work. Calculators are not allowed, except as indicated below. 1. (5 marks) The speedometer reading (v) on a car was observed through a 10-minute period at 1-minute intervals and recorded in the table below. Use Simpson’s Rule to estimate the distance travelled by the car. (The total distance travelled is the integral of the velocity. All readings are in kilometers per hour. In this problem, you may use a calculator.) t 0 1 2 3 4 5 6 7 8 9 10 v 56 58 62 61 64 66 63 60 61 63 61 2. Z ∞(5 marks) We dx √ , but 1 + x6 1 Use a substitution on page 398 of the want to use a numerical method (eg. Simpson’s Rule) to evaluate we can’t do it directly because the interval of integration is infinite. to convert this integral to one over a finite interval (see the examples textbook). 3. (10 marks) Calculate the volume of each solid, using either slices or cylindrical shells, whichever you prefer: (a) The solid generated by rotating about the x-axis the region bounded by the curves y = cos x, y = sin x, and the lines x = 0, x = π/4. (b) The solid generated by rotating about the y-axis the region bounded by the curve y = ex , and the lines x = 1, y = 1. This homework covers Sections 6.7–6.8 and 7.1 of the textbook. Additional recommended exercises: Section 6.7: 1–10; Section 6.8: 1–9; Section 7.1: 1–23. 1