Using n=6 approximate the value of ∫_(-1)^2▒√(e^(-x^2 )+1) dx using Trapezoid rule. (6) Using n 6 approximate the value of L3 Ve-x2 + 1 dx using Trapezoid rule. 15Marks
2. Use the Trapezoid rule with n = 4 subintervals to approximate the integral (i.e approximate In 3). Round your answer to 4 decimal places (or give a simplified fraction). An answer without work will not receive credit; you must write out the expression you put into a calculator. 3. In 1311.098012389 dr -- inixl1,° - inixll,
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...
Problem 10. (1 point) 5." -4 sin x dx a) Approximate the definite integral with the Trapezoid Rule and n = 4. b) Approximate the definite integral with Simpson's Rule and n = 4. c) Find the exact value of the integral.
Question 11 Not yet answered Use the Trapezoid rule to evaluate x?dx, partitioning the interval of integration into n = 4 subintervals of equal width Ax = 1 Points out of 2.00 P Flag question Select one: O a. 42 O O b. 60 c. 22 d. 32 e. 70
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?...
3. Suppose we want to use the ri-term trapezoid rule to approximate Sinde (a) (3 points) Make a graph of y= between = 2 and 3 = 4. Draw on your graph the trapezoids used to apply the Trapezoidal Rule with n = 3. (So, your graph should have 3 trapezoids.) (b) (2 points) Does the Trapezoidal Rule overestimate or underestimate the value of justify your answer. 1 dx? No need to (c) (5 points) For the Trapezoidal Rule, the...
Problem 4. (15 points) Use the trapezoid rule with h = { to approximate the integral 1 = To vi+ x4 ax How small does h have to be for the error to be less than 10-3?
Consider the following integral: S“ sinº (0) do (a) Use the Trapezoid Rule with n = 6 to approximate the integral. (b) Use Simpson's Rule with n = 6 to approximate the integral.
1. Use the Midpoint Rule with n = 6 to approximate the integrale dx . Round the final answer to 6 decimal places.