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i need help with 1,3,5. i dont quite know when to use midpoint or the trapezoidal...
EXAMPLE 5 Use the Midpoint Rule with n = 5 to approximate the following integral. dx х SOLUTION The endpoints of the subintervals are 1, 1.6, 2.2, 2.8, 3.4, and 4, so the midpoints are 1.3, 1.9, 2.5, 3.1, and width of the subintervals is Ax = (4 - 175 so the Midpoint Rule gives The 1.9* 2s 313) dx Ax[f(1.3) + (1.9) + (2.5) + F(3.1) + f(3.7)] -0.06 2 + 1.3 2.5 3.1 . (Round your answer to...
4) (25 pts) Evaluate the integral d: +5 Using the following methods: a) Analytically b) Trapezoidal rule. Divide the whole interval into four subintervals (n 4) c) Simpson's 1/3 rule. Divide the whole interval into four subintervals (n 4). d) Simpson's 3/8 rule. Divide the whole interval into three subintervals (n 3) Compare the results in b), c), and d) with the true value obtained in a). 4) (25 pts) Evaluate the integral d: +5 Using the following methods: a)...
Estimate the area of the region bounded by the graph of f(x)-x + 2 and the x-axis on [0,4] in the following ways a. Divide [0,4] into n = 4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the solution geometrically. b. Divide [0,4] into n = 4 subintervals and approximate the area of the region using a midpoint Riemann sum· illustrate the solution geometrically. C. Divide [04] into n = 4 subintervals and...
The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate f(x) dx, where f is the function whose graph is shown below. The estimates were 0.7811 0.8675, 0.8632, and 0.9540, and the same number of subintervals were used in each case. (a) Which rule produced which estimate? ?1. Trapezoidal Rule estimate 2. Right-hand estimate 3. Left-hand estimate N4. Midpoint Rule estimate (b) Between which two approximations does the true value of o fa) dx lie? A. 0.8675 β...
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) 5 3 cos(6x) n = 8 dx, X 1 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule
need help. please amswer #3 and 4 • The Midpoint Rule. Trapezoidal Rule. • Simpson's Rule. 2. Using n = 4, approximate the value of وت using all three rules. 3. Using n = 4, approximate the value of 1 l, dc 1+r2 using all three rules. 4. Using n = 4, approximate the value of L using all three rules.
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral 11 ln(2) 5," dx 5 + x with n= = 6. T6 = M6 = S6 =
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) 1/2 0 10 sin(x2) dx, n = 4
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places. pi/2 3sqrt(1 + cos(x))dr, n = 4 0
I only need help with calculating the midpoint riemann sum at the very bottom using the fx=x^2+1 on [2;6]; n=4 c. Illustrate the midpoint Riemann sum by sketching the appropriate rectangles. d. Calculate the midpoint Riemann sum. f(x) = x2 +1 on [2,6); n=4 List the grid points. (Use a comma to separate answers as needed. Simplify your answers.) c. Illustrate the midpoint Riemann sum. Choose the correct graph below. 31 OA. OB. 40- Q 250 - 250- Q Q...