Practice: Area Under a Curve-Trapezoidal Rule · 2020. 4. 23. · 1. Use left the Trapezoidal Rule to estimate the area under the curve between . x =−1 and . x =2 ... from 0 to

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

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.