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doan (bad696) – 5.1 – Stepp – (56510) 1 This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Estimate the area under the graph oF f ( x ) = sin x between x = 0 and x = π 2 using fve approx- imating rectangles oF equal widths and right endpoints. 1. area 1 . 169 2. area 1 . 109 3. area 1 . 189 4. area 1 . 149 correct 5. area 1 . 129 Explanation: An estimate For the area under the graph oF f on [0 , b ] with [0 , b ] partitioned in n equal subintervals [ x i - 1 , x i ] = b ( i - 1) b n , ib n B and right endpoints x i as sample points is A ± f ( x 1 ) + f ( x 2 ) + . . . + f ( x n ) ² b n . ±or the given area, f ( x ) = sin x, b = π 2 , n = 5 , and x 1 = 1 10 π, x 2 = 1 5 x 3 = 3 10 x 4 = 2 5 x 5 = 1 2 π . Thus A ± sin p 1 10 π P + . . . + sin p 1 2 π π 10 . AFter calculating these values we obtain the estimate area 1 . 149 For the area under the graph. keywords: area, sin Function, estimate area, numerical calculation, 002 10.0 points Rewrite the sum ± 3+ p 1 9 P 2 ² + ± 6+ p 2 9 P 2 ² + . . . + ± 21+ p 7

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