Question 3 Given the function () x2 +05 find the numerical integration from a -1.5 to...
Written Essay on Module 4: Applications of Integration & Numerical Integration, Due May 2 5. (10 points) For both graphs below, use (i) Trapezoidal Rule, and (ii) Simpson's Rule with a sub- division into n = 4 subintervals to estimate the area under the given curves on the interval (1,5). (iii) In each case, determine which rule is more accurate. Explain why. (a) y = f(x) (b) y = g(x)
7. (15 pts) Numerical Integration. Given a continuous function f (x) on the interval [a, b], write the Lagrange form of the quadratic polynomial interpolating f(a), (a b)), f(b). Instead of calculating the integral I(f) Jaf(x)dx we could approximate it via Q(f) = | q(x)dx. Find an expression for this quadrature rule, the so-called Simpson's rule.
1. Numerical Integration The integral of a function f(x) for a s x S b can be interpreted as the area between the f(x) curve and the x axis, bounded by the limits x- a and x b. If we denote this area by A, then we can write A as A-f(x)dx A sophisticated method to find the area under a curve is to split the area into trapezoidal elements. Each trapezoid is called a panel. 1.2 0.2 1.2 13...
please answer question 5. question 4 is provided for reference.
Problem 5: Application of composite integration rules Assume that you want to approximate the integral of a function in [0, 21 and have only the values of f on specific x values, given in the following table. x005 11.5| 2 (a) Find an approximation to f(x) dx using the composite trapezoid integration rule. Specify all parameters of the approximation and carry out the calculation completely. Assignment 8 MATH363, Spring 2019...
Please I need help in solving numerical differentiation, numerical integration and finding the extrema, Using PYTHON. Question: Given a function
Q3 ) Use numerical integration with n=3 to determine the following integration then solve it analytically using a proper method of integration and compare results. Inx dx
Q3 ) Use numerical integration with n-3 to determine the following integration then solve it analytically using a proper method of integration and compare results. InLX dx 04) Used double integral find the area between the following curves y = x2y = 2 - x (5) Use shell method find the volume of the solid generated by revolving the curves y=x", y = 2 - x?, about y axis
A marginal revenue function MR(x) (in dollars) is given below. Use numerical integration on a graphing calculator or computer to find the total revenue over the given range. 195 MR(x) = 7+2 1 +2 -0.8x – 25, 0 sxs 270 -0.8% . The total revenue over the given range is approximately $ (Round to the nearest cent as needed.)
using the general power rule
Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2 3(x2+x)2 (2x+1) • (x2+x)2 (2x+1) recall general power rule formula has three parts: [u(x)" ]' = n u(x)" 1 u'(x) Question 2 let y = (x3 +x2) 1/3 Find y' (x3 +x2) 1/3 (1/3) (x3 +x2) 1/3 . (1/3)(x3 +x2)-2/3 (1/3)(x3 +x2-2/3 (3x2+2x) recall general power rule has three parts. [u(x)"l' = n u(x)n-1 u'(x) Question 5 let g(x) = 1/(x3+x2)3 find g'(x) (x²+x23...
11. (10pts) Consider the curve given by the function f(x) = x2 – 3x + 2 a) Approximate the area of the curve over the interval [0,10) using Reimann Sums. Use midpoints with n = 5 subintervals. b) Find the exact area of the curve over the interval [0,10] using integration.