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eee If a 100-foot lake's width is measured at 10-foot intervals (as shown), approximate the area of the lake using the Trapezoidal Rule.
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| eee Figure shows the measured rate of water flow ( in liters per minute ) in to a tank during a 10-min period. Using 10 subintervals in each case, estimate the total amount of water that flows into the tank during this period by using the trapezoidal approximation. eee |
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eee Figure shows the daily mean temperature recorded during December at Big Frog, California. Using 10 subintervals in each case, estimate the average temperature during that month by using the trapezoidal approximation.
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| eee Approximate the area between the curve f(x) = x3- x + 1 and the x-axis on the interval [0, 2] using 4 rectangles and the Trapezoidal Rule. eee |
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eee Below is a chart representing John's rate of hair loss (in follicles per day) on various days throughout a two-week period. Use 6 trapezoids to approximate John's total hair loss over the 14-day period.| Day | Hair Loss | | 1 | 2 | | 4 | 7 | | 6 | 9 | | 9 | 5 | | 11 | 13 | | 13 | 17 | | 14 | 21 |
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eee f(x) is a continuous function whose values are given in the table.
| x | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | | f(x) | 29 | 26 | 22 | 17 | 14 | 11 | 19 | 24 | 28 |
By using the trapezoidal method with trapezoids of width 5, approximate ∫545f(x) dx.
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eee The speed (v) - time(t) graph of a car is shown. Approximate the distance travelled by the car using the trapezoidal rule.
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| eee Calculate the trapezoidal approximation to the integral ∫03x2dx with n = 6 and Δx = 0.5. eee |
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eee Calculate the trapezoidal approximation Tn to the integral ∫04xdx. Using 4 subintervals.
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eee Calculate the trapezoidal approximation Tn to the integral ∫01xdx. Use n = 5 subintervals and round the answer to two decimal places.
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| eee Calculate the trapezoidal approximation Tn to the integral ∫45x2dx. Use n = 5 subintervals and round the answer to two decimal places. eee |
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| eee Calculate the trapezoidal approximation Tn to the integral ∫0π/2cosxdx. Use n = 3 subintervals and round the answer to two decimal places. eee |
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eee Calculate the trapezoidal approximation Tn to the integral. ∫41x3dx Use n = 6 subintervals and round the answer to two decimal places.
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| eee Calculate the trapezoidal approximation Tn to the integral ∫0πsinxdx. Use n = 4 subintervals and round the answer to two decimal places. eee |
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| eee Calculate the trapezoidal approximation Tn to the integral ∫13x2 (1 + x)dx. Use n = 4 subintervals and round the answer to two decimal places. eee |
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eee Calculate the trapezoidal approximation Tn to the integral ∫15 1xdx. Use n = 8 subintervals and round the answer to two decimal places.
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eee Calculate the trapezoidal approximation Tn to the integral ∫021+x3dx. Use n = 6 subintervals and round the answer to two decimal places.
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| eee Calculate the trapezoidal approximation Tn to the integral ∫0π/3tan xdx. Use n = 5 subintervals and round the answer to two decimal places. eee |
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eee Calculate the trapezoidal approximation Tn to the integral ∫0311+x4dx. Use n = 6 subintervals and round the answer to two decimal places.
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eee Calculate the trapezoidal approximation Tn to the integral ∫212x(x + 1)2dx. Use n = 5 subintervals and round the answer to two decimal places.
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eee Calculate the trapezoidal approximation of ∫abf(x)dx where f(x) is the given tabulated function | x | 1.00 | 1.25 | 1.50 | 1.75 | 2 | 2.25 | 2.5 | | f(x) | 3.43 | 2.17 | 0.38 | 1.87 | 2.65 | 2.31 | 1.97 |
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eee Calculate the trapezoidal approximation of ∫abf(x)dx where f is the given tabulated function | x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | | f(x) | 23 | 8 | 4 | 12 | 35 | 47 | 53 | 50 | 39 | 29 | 5 |
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eee Calculate the trapezoidal approximation of ∫abf(x)dx where f(x) is the given tabulated function | x | 0 | 50 | 100 | 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 | | f(x) | 0 | 165 | 172 | 200 | 300 | 512 | 190 | 150 | 125 | 136 | 140 |
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eee Calculate the trapezoidal approximation of ∫abf(x)dx where f is the given tabulated function | x | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | | f(x) | 0 | 5 | 6 | 7 | 2 | 3 | 1 |
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eee Suppose that the graph in figure shows the velocity v(t) recroded by instruments on the board of a submarine traveling under the polar ice cap directly towards the north pole. Use the trapezoidal approximation to estimate the distance s = ∫abv(t)dt traveled by the submarine during the 10-hour period from t = 0 to t = 10.
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