Find an approximation to {image} Use a double Riemann sum with m = n = 2 and the sample point in the lower left corner to approximate the double integral,

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Presentation transcript:

Find an approximation to {image} Use a double Riemann sum with m = n = 2 and the sample point in the lower left corner to approximate the double integral, where {image} -2,820 -2,795 -188 -2,818 -2,828 -2,824 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Let V be the volume of the solid that lies under the graph of {image} and above the rectangle given by {image} We use the lines x = 0 and y = 2 to divide R into subrectangles. Find the Riemann sum using lower left corners. Select the correct answer. The choices are rounded to the nearest hundredth. 83.42 31.46 10.34 114.75 10.3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Evaluate the double integral by first identifying it as the volume of a solid. {image} {image} 180 5,040 -118 90 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Use the Midpoint Rule with one square of to estimate {image} where {image} Use 2.72 to approximate e. 0.000092 0.548132 0.274066 0.924334 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50