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1 Find the midpoint and trapezoid rule approximations to S cos zxdx using n=25 subintervals. Compute...
Find the midpoint rule approximations to the following integral. 3 X dx using n 1, 2, and 4 subintervals. 1 M(1)- (Simplify your answer. Type an integer or a decimal.) Find the midpoint rule approximations to the following integral. 3 X dx using n 1, 2, and 4 subintervals. 1 M(1)- (Simplify your answer. Type an integer or a decimal.)
Find the indicated Midpoint Rule approximation to the following integral. 12 S22 2x dx using n=1, 2, and 4 subintervals 4 12 The Midpoint Rule approximation of S xx? dx with n= 1 subinterval is (Round to three decimal places as needed.)
Find the midpoint rule approximations to the following integral. 12 S x x3dx using n= 1, 2, and 4 subintervals. 4 M(1) = (Simplify your answer. Type an integer or a decimal.) M(2) = (Simplify your answer. Type an integer or a decimal.) M(4) = (Simplify your answer. Type an integer or a decimal.)
Apply Simpson's Rule to the following integral. It is easiest to obtain the Simpson's Rule approximations from the Trapezoid Rule approximations. Make a table showing the approximations and errors for n 4, 8, 16, and 32. The exact value of the integral is given for computing the error. Sax-2) dx 1920 Complete the table below. (Type integers or decimals. Round to two decimal places as needed.) Absolute Error in T(n) Absolute Error in T(n) S(n) S(n) 4 Apply Simpson's Rule...
Let f(x) = cos(x2). Use (a) the Trapezoidal Rule and (b) the Midpoint Rule to approximate the integral ſo'f(x) dx with n = 8. Give each answer correct to six decimal places. To Mg = (c) Use the fact that IF"(x) = 6 on the interval [0, 1] to estimate the errors in the approximations from part (a). Give each answer correct to six decimal places. Error in Tg = Error in Mg = (d) Using the information in part...
Given the integral below, do the following. 2 cos(x2) dx Exercise (a) Find the approximations T4 and M4 for the given interval. Step 1 The Midpoint Rule says that b f(x) dx = Mn Ax[f(+1) + f(22) + ... + f(n)] with ax = . b - a + n a 1 We need to estimate 6 2 cos(x2) dx with n = 4 subintervals. For this, 1 - 0 Ax = 4 = 1/4 1/4 Step 2 Let žų...
Question involving Simpon's rule, Midpoint rule, and the error bound rule. How do I solve for b), d), and g)? Let f(x)-ecos(x) and 1 -Ís2π f(x) dx (a) Use M1o to approximate I to six decimal places. M17.95492651755339 (b) Use the fact that |f"(x)| e on [0, 2T to obtain an upper bound on the absolute error EM of the approximation from (a). Make sure your answer is correct to six decimal places EM0.16234848503 (c) Use Si0 to approximate I...
Let EM represent the error in using the Midpoint Rule with subintervals to approximate S. f(x) dx. Then K(b - a) TEM 24n2 where K is the maximum number that the absolute value of IF"(x) achieves for asx<b. Use this inequality to find the minimum number, 17 of subintervals necessary to guarantee that the Midpoint Rule will approximate the integral dx to be accurate to within 0.001. 80 O 358 253 114
Estimate 5 cos(x2) dx using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round your answers to six decimal places.) (a) the Trapezoidal Rule 4.476250 x (b) the Midpoint Rule 4.544562 x From a graph of the integrand, decide whether your answers are underestimates or overestimates. T4 is an underestimate O T4 is an overestimate O M4 is an underestimate O M4 is an overestimate
Problem 3. Suppose you are programming the composite trapezoid rule (CTR) to approximate 1(f) =| f(x) dx using the TR with N subintervals, and that you mistakenly forget to weight down the two endpoints by 3. That is, you have accidentally programmed the quadrature rule where h-%.. (Note: sinoefe C, you know that UIL is bounded.) 1. Find QBADN -OCTRN where QCTRN ) is the approximation to (x) dx computed via the CTR with N subintervals. Problem 3. Suppose you...