1. The natural logarithm of (x > 0) can be computed using In(x) dt. Use (a)...
Question 1: Numerically integrate function f(x) given on the right from x=0 to x=10. Use the f(x)= x2 - 6x + 16 Trapezoidal Rule and the Simpson's 1/3 Rule and compare the results. Use at least 4 50 + 15x - ye? decimal digits in your calculations and reporting. Organize and report each one of your solutions in a calculation table and identify your result clearly. a) Divide the interval into 5 subdivisions. Calculate the integral first using the Trapezoidal...
Question Part Points Submissions Used 1 2 3 0/1 –/1 –/1 1/15 0/15 0/15 Total 0/3 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.) 4 e2√t sin(4t) dt, n = 8
1) The integral l = Jo sinx dx is important in the design of precise photographic lenses (among other applications). The function fx)hoever, has no elementary antiderivative, so The sir Fundamental Theorem of Calculus cannot be used to calculate the value of the integral. Use the Trapezoidal Rule, the Midpoint Rule and the Simpson's Rule to approximate the numerical value of the integral. Use n 10. 2) The following data shows the velocity vit) recorded by instruments on board a...
Use Matlab code Consider the following function sin(x) Using the following parameters in your functions: -func: the function/equation that you are required to integrate -a, b: the integration limits n: the number of points to be used for the integration I:Integral estimate a) Write a function capable of performing numerical integration of h(x) using the composite trapezoidal rule. Use your function to integration the equation with 9 points. Write a function capable of performing numerical integration of h(x) using the...
Need help with #9 and #10 Question 9 B0/1 pt 1099 Details 1 Approximate dx using the midpoint rule with In(x) five subdivisions to four decimal places. es, The approximation is: Question Help: Message instructor Submit Question Question 10 B0/1 pt 3 10 399 Details Use Simpson's Rule and all the data in the following table to estimate the value of the integrat ]," f(a)dz. f(x) 9 6 10 х 9 11 13 15 17 19 21 4 2 1...
Numeric Analysis 1) Letf(x)=- 2x x2-4 a. Approxi the first derivative using central difference and the second derivative mate at x= 1.25 using and h=0.25. (Use 4 decimal digits using backward difference rounding). Approximate f f(x)dx using trapezoidal rule with h-0.5 (Use four decimal digits rounding) c. Approximate S fCx)dxusing 1/3 Simpson's rule with h-0.25 (Use four decimal digits rounding)
Multiple choices Use Gaussian Quadrature to find the value of the integral of: f(x) = 79.13 / ( 5.30 + 2.24 * X * X) between X= -0.62 and X= 1.55 Integral using 2 terms Gaussian Quadrature is Integral using 3 terms Gaussian Quadrature is l__ Integral using 4 terms Gaussian Quadrature is Integral using 6 terms Gaussian Quadrature is Use the trapezoidal rule to find the value of the integral of: f(x) = 63.52 / ( 4.07 + 2.23...
MATLAB Create a function that provides a definite integration using Simpson's Rule Problem Summar This example demonstrates using instructor-provided and randomized inputs to assess a function problem. Custom numerical tolerances are used to assess the output. Simpson's Rule approximates the definite integral of a function f(x) on the interval a,a according to the following formula + f (ati) This approximation is in general more accurate than the trapezoidal rule, which itself is more accurate than the leftright-hand rules. The increased...
3. (25 Points) Find f(t). f(0) + f(t - 1)f(t)dt = t. Hint: The second term on the left side is a convolution and it might be helpful to use the Laplace Transform. 1 4. (10 Points) Solve the initial value problem by Laplace transform techniques. x" + 5x' + 4x = 0;x(0) = 1,x'(0) = 0. I 5. (15 Points) Find a series solution for the following differential equation. Calculate the radius of convergence. 2(x - 1)y' = 3y...