Practice: Area Under a Curve-Trapezoidal Rule Name: ______________________________ Directions: Estimate the area under the curve using Riemann sums as indicated. 1. Use left the Trapezoidal Rule to estimate the area under the curve between 1 x =− and 2 x = using 3 equal subintervals 2. Use Trapezoidal Rule to estimate the area under the curve between 2 x =− and 4 x = using three equal subintervals 3. Use Trapezoidal Rule to estimate the area under the curve between 2 x =− and 3 x = using 5 equal subintervals 4. Use Trapezoidal Rule to estimate the area under the graph of () 4 fx x = − between 4 x = and 13 x = using three equal subintervals 5. The function f is continuous on the closed interval [ ] 0,10 and has values that are given in the table below. Using four subdivisions, estimate the area under the curve on this interval using trapezoids. (they don’t have to be equal) x 0 1 4 8 10 ( ) f x 4 5 10 12 8 6. An approximation of the area under the curve 3 y x = from 0 to 4 using the Trapezoid Rule with four equal subintervals is A. 34 B. 68 C. 50 D. 136
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Practice: Area Under a Curve-Trapezoidal Rule
Name: ______________________________ Directions: Estimate the area under the curve using Riemann sums as indicated.
1. Use left the Trapezoidal Rule to estimate the area under the curve between 1x = − and 2x = using 3 equal subintervals
2. Use Trapezoidal Rule to estimate the area under the curve between 2x = − and 4x = using three equal subintervals
3. Use Trapezoidal Rule to estimate the area under the curve between 2x = − and 3x = using 5 equal subintervals
4. Use Trapezoidal Rule to estimate the area under the graph of ( ) 4f x x= − between 4x = and 13x = using three equal subintervals
5. The function f is continuous on the closed interval [ ]0,10 and has values that are given in the table below. Using four subdivisions, estimate the area under the curve on this interval using trapezoids. (they don’t have to be equal)
x 0 1 4 8 10 ( )f x 4 5 10 12 8
6. An approximation of the area under the curve 3y x= from 0 to 4 using the Trapezoid Rule with
four equal subintervals is
A. 34 B. 68 C. 50 D. 136
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Practice: Area Under a Curve-Trapezoidal Rule
7. In the table below, F is the force in pounds acting on an object in its direction of motion and x is the displacement of the object in feet. Use the Trapezoidal Rule to approximate the work done by the force in moving the object from 0x = to 50x = . (Work=force * distance)
x 0 5 10 15 20 25 30 35 40 45 50 F 100 80 66 56 50 45 40 36 33 30 28
8. In the table below, S is the area in square meters of the cross section of a railroad track cutting through a mountain and x meters is the corresponding distance along the line. Us the Trapezoidal Rule to find the number of cubic meters of earth removed to make the cutting from 0x = to 150x = .
x 0 25 50 75 100 125 150 S 105 118 142 120 110 90 78
9. The function ( ) 2xf x e−= on the interval [ ]0,1 is partitioned into four sub intervals: 1 1 1 1 3 30, , , , , , ,14 4 2 2 4 4
. Use the Trapezoidal Rule to estimate the area under the curve.
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