2. Since it is difficult to evaluate the integral / e dx exactly, we will approximate it using Maclaurin 0 polynomials...
2. Since it is difficult to evaluate the integral dr exactly, we will approximate it using Maclaurin polynomials (a) Determine P4(x), the 4th degree Maclaurin polynomial of the integrand e". (b) Obtain an upper bound on the error in the integrand for r in the range 0-x 1/2, when the integrand is approximated by Pi(x). (c) Find an approximation to the original integral by integrating P4(r (d) Obtain an upper bound on the error in the integration in (c) (e)...
2. Since it is difficult to evaluate the integrae dz exactly, we will approximate it using Maclaurin polynomials polynomial of the integrand et (a) Determine P(x), the 4th degree Maclaurin (b) Obtain an upper bound on the error in the integrand for z in the range 0 S 1/2, when the integrand is approximated by Pa(x) (c) Find an approximation to the original integral by integrating P(x). (d) Obtain an upper bound on the error in the integration in (c)....
Since t is difficult to evaluate the integral e dx exactly, we will approximate t using Maclaurınn polynomials 2 (a) Determine P4(x), the 4th degree Maclaurin polynomial of the integrand e" (b) Obtain an upper bound on the error in the integrand for r in the range 0S S 1/2 (c) Find an approximation to the original integral by integrating P4(x) (d) Obtain an upper bound on the error in the integration in (c) 2, when the integrand is approximated...
1. Suppose that we would like to approximate Sof(x)dx by QU) = 0 P2(x)dx, (1) where P2(x) is the polynomial of degree at most two which interpolates f at 0, 1/2, and 1. (a) Write P2(x) in Lagrange form and prove that Q[F] o [s0 f(0) + 4f 45 (2) +scn)] (2) (b) Consider now a general interval [a, b] and the integral só f(x)dx. Do the change of variables x = a + (b − a)t to transform the...
Sec6.5: Problem 6 Previous Problem List Next (2 points) Book Problem 17 4, to approximate the integral 7e dx (a) Use the Midpoint Rule, with n MA (Round your answers to six decimal places.) (b) Compute the value of the definite integral in part (a) using your calculator, such as MATH 9 on the TI83/84 or 2ND 7 on the TI-89. 7edx (c) The error involved in the approximation of part (a) is Ем — Те ах Ма (d) The...
QUESTION 5 The integral 2 1 I= dx x +4 0 is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite Trapezoidal rule, given by -haf" (), a< & <b, 12 is less than 10-5 for the approximation of I. b - a (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are ci = 1, i...
10. Trapezoidal Rule is used to approximate the integral f(a) dx using 1- (yo +2y1 + 2y2 + x-na b-a + 2yn-1 +%),where Use this approximation technique to estimate the area under the curve y = sinx over。 a. π with n 4 partitions. x A 0 B: @ Δy B-A b. The error formula for the trapezoidal rule is RSL (12ba)1 where cischosen on the interval [a, b] to maximize lf" (c)l. Use this to compute the error bound...
(a) i) For ∫(4x−4)(2x^2-4x+2)^4 dx (upper boundry =1, lower =0) Make the substitution u=2x^2−4x+2, and write the integrand as a function of u, ∫(4x−4)(2x^2−4x+2)^4 dx =∫ and hence solve the integral as a function of u, and then find the exact value of the definite integral. ii) Make the substitution u=e^(3x)/6, and write the integrand as a function of u. ∫ e^(3x)dx/36+e^(6x)=∫ Hence solve the integral as a function of u, including a constant of integration c, and then write...
Evaluate the integral using integration by parts. e4 Sx x? In (x)dx 1 e 4 S x In (x)dx=0 (Type an exact answer.)
For the final project, you will create an integral calculator polynomials of degree zero, one, two three and four Degree Function yz where z is a constant 3 where a,b.c.d.z e R, real numbers You will ask the user for the degree of the polynomial and then the coefficients and the constant values of the polynomial. Then you will ask the user for the beginning and the end of the interval along with the number of steps between the interval...