Find the indicated Midpoint Rule approximation to the following integral. 12 S22 2x dx using n=1,...
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.)
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...
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.)
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.)
& Evaluate the following integral by completing the square and using a substitution to reduce it to standard form. dx S (x + 1)Wx2+ + 2x - 15 dx S (x+1)\x² + 2x – 15 f(t) = cos(t/2 - 31/8) 12 Approximate the area of the region bounded by the graph of f(t) = cos (t/2-31/8) and the t-axis on [0,1] with n = 4 subintervals. Use the midpoint of each subinterval to determine the height of each rectangle (see...
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...
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.) S 2 + cos(x) dx, n=4 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read Talk to Tutor
4. Another approximation for integrals is the Trapezoid Rule: integral (a to b)f(x) dx ≈ ∆x/2 (f(x_0) + 2f(x_1) + 2f(x_2) + · · · + 2f(x_n−2) + 2f(x_(n−1)) + f(x_n)) There is a built-in function trapz in the package scipy.integrate (refer to the Overview for importing and using this and the next command). (a) Compute the Trapezoid approximation using n = 100 subintervals. (b) Is the Trapezoid approximation equal to the average of the Left and Right Endpoint approximations?...
use trapezoidal, midpoint and simpsons rule given the following integral (the power in front of the radical is a 4) وه 15+ r?dx, n = 8 (a) Use the Trapezoidal Rule to approximate the given integral with the specified value of n. (Round your answer to six decimal places.) (6) Use the Midpoint Rule to approximate the given integral with the specified value of n. (Round your answer to six decimal places.) (c) Use Simpson's Rule to approximate the given...
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