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Unformatted text preview: 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 find all choices before answering. 001 10.0 points Estimate the area under the graph of f ( x ) = sin x between x = 0 and x = 2 using five 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 ] = bracketleftBig ( i- 1) b n , ib n bracketrightBig and right endpoints x i as sample points is A braceleftBig f ( x 1 ) + f ( x 2 ) + . . . + f ( x n ) bracerightBig b n . For the given area, f ( x ) = sin x, b = 2 , n = 5 , and x 1 = 1 10 , x 2 = 1 5 , x 3 = 3 10 , x 4 = 2 5 , x 5 = 1 2 . Thus A braceleftBig sin parenleftBig 1 10 parenrightBig + . . . + sin parenleftBig 1 2 parenrightBigbracerightBig 10 . After calculating these values we obtain the estimate area 1 . 149 for the area under the graph....
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This note was uploaded on 01/28/2010 for the course 408L 56510 taught by Professor Stepp during the Spring '10 term at University of Texas at Austin.

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solution_pdf - doan (bad696) 5.1 Stepp (56510) 1 This...

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