Find the midpoint rule approximations to the following integral. 3 X dx using n 1, 2, and 4 subintervals. 1 M(1)- (...
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.)
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.)
1 Find the midpoint and trapezoid rule approximations to S cos zxdx using n=25 subintervals. Compute the relative error of each approximation. 0 T(25) (Do not round until the final answer. Then round to six decimal places as needed.)
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...
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...
Approximate the integral below using 4 subintervals and: (x + 1) dx (a) The Simpson's rule (5 points): (b) Compare your estimate with the exact value of the integral. (5 points)
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...
3 11 Use Simpson's rule with n=1 (so there are 2n = 2 subintervals) to approximate dx. 1 + x2 The approximate value of the integral from Simpson's rule is (Round the final answer to two decimal places as needed. Round all intermediate values to four decimal places as needed.) 5 Use Simpson's rule with n=4 (so there are 2n = 8 subintervals) to approximate OX dx and use the fundamental theorem of calculus to find the exact value of...
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
The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate r(x) dx, where f is the function whose graph is shown. The estimates were 0.7819, 0.8664, 0.8631, and 0.9510, and the same number of subintervals were used in each case. y=f(x) (a) Which rule produced which estimate? Ln - Rn- To- Mn- fx) dx lie? (b) Between which two approximations does the true value of (smaller value) (larger value) The left, right, Trapezoidal, and Midpoint Rule approximations were...