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DDD 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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| DDD 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. DDD |
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DDD 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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| DDD 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. DDD |
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DDD 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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DDD 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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DDD 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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| DDD Calculate the trapezoidal approximation to the integral ∫03x2dx with n = 6 and Δx = 0.5. DDD |
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DDD Calculate the trapezoidal approximation Tn to the integral ∫04xdx. Using 4 subintervals.
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DDD 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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| DDD Calculate the trapezoidal approximation Tn to the integral ∫45x2dx. Use n = 5 subintervals and round the answer to two decimal places. DDD |
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| DDD Calculate the trapezoidal approximation Tn to the integral ∫0π/2cosxdx. Use n = 3 subintervals and round the answer to two decimal places. DDD |
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DDD 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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| DDD Calculate the trapezoidal approximation Tn to the integral ∫0πsinxdx. Use n = 4 subintervals and round the answer to two decimal places. DDD |
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| DDD Calculate the trapezoidal approximation Tn to the integral ∫13x2 (1 + x)dx. Use n = 4 subintervals and round the answer to two decimal places. DDD |
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DDD 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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DDD 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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| DDD Calculate the trapezoidal approximation Tn to the integral ∫0π/3tan xdx. Use n = 5 subintervals and round the answer to two decimal places. DDD |
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DDD 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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DDD 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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DDD 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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DDD 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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DDD 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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DDD 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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DDD 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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