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Use the Trapezoidal Rule with n trapezoids to approximate the following integrals. R 1 sin(5x2. 0 1) dx, n = 5. R 17. ln(x + 2) dx, n = 5. R 2:1 pj cos xj dx, n = 3.
5 paź 2023 · Single and composite applications of the trapezoidal rule to approximate the value of definite integrals. Error analysis of the trapezoidal rule.
the trapezoidal rule has the form Zb a f (x)dx ˇ h 2 [y0 +2y1 +2y2 +. . . +2yn 1 +yn] (1) where 1. n is the number of strips and can be any number. 2. yn = f (xn) are the values of f (xn) at the points xi where i = 0,1,2,. . .,n. Note that x0 = a, xn = b. 3. h is the width of each strip and h = b a n. 4. x1 = a+h, x2 = a+2h, x3 = a+3h ...
Worksheet 14, Math 10560 1 Use the trapezoidal rule with step size x = 2 to approximate the integral R 4 0 f(x)dx where the graph of the function f(x) is given below. 1 2 3 4 1 2 3 4 Solution: Note n = 4 0 2 = 2: Then by the trapezoidal rule Z 4 0 f(x)dx ˇ x 2 (f(x 0) + 2f(x 1) + f(x 2)) = 2 2 (2 + 8 + 0) = 10:
Trapezoidal Rule Practice For each problem, approximate the area under the curve over the given interval using 4 trapezoids. 1) y = x + 6; [ 1, 5] 36 2) y = x + 4; [ −2, 2] 16 For each problem, approximate the area under the curve over the given interval using 5 trapezoids. 3) y = −x2 − 2x + 9; [ −3, 2] 75 2 = 37.5 4) y = 2 x; [ 2, 7 ...
(b) Use the trapezium rule with all the values of y in the completed table to obtain an estimate for the area of the shaded region R, giving your answer to 4 decimal places.
1. Figure 1. y. Figure 1 shows the graph of the curve with equation. y = xe2x, x 3 0. The finite region R bounded by the lines x = 1, the x-axis and the curve is shown shaded in Figure 1. (a) Use integration to find the exact value of the area for R. (5) (b) Complete the table with the values of y corresponding to x = 0.4 and 0.8. (1)
