In this question, you will estimate the value of the integral S xe-dr using three different approximations. a. Subdivide the interval [0,3] into three sub-intervals of equal width and complete the following: Ax = |f(ao) = |f(a₁)= |f(a₂) = |f(a3) = f(x₁) = f(x₂) f(x3) = ao = a₁ = a2 = a3 = X1 = x2 = x3 = b. Calculate the approximate value of the integral using the trapezoidal rule. Area = c. Calculate the approximate value of the integral using the midpoint rule. Area

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In this question, you will estimate the value of the integral
-3
xe-5 dr
dx
using three different approximations.
a. Subdivide the interval [0,3] into three sub-intervals of equal width and complete the following:
Ax:
ao =
a₁ =
a2 =
a3
X1 =
x2 =
X3 =
b. Calculate the approximate value of the integral using the trapezoidal rule.
Area
=
||
|f(ao) =
=
|f(a₁) =
|f(a₂) =
|f(a3) =
f(x₁) =
f(x₂)=
|f(x3)=
c. Calculate the approximate value of the integral using the midpoint rule.
Area
d. Calculate the approximate value of the integral using Simpson's rule.
Area
e. It is possible to show that an antiderivative of x e-*/3 is
−3(x+3) e-3
Using this antiderivative, calculate the exact value of the integral.
Integral =
Transcribed Image Text:In this question, you will estimate the value of the integral -3 xe-5 dr dx using three different approximations. a. Subdivide the interval [0,3] into three sub-intervals of equal width and complete the following: Ax: ao = a₁ = a2 = a3 X1 = x2 = X3 = b. Calculate the approximate value of the integral using the trapezoidal rule. Area = || |f(ao) = = |f(a₁) = |f(a₂) = |f(a3) = f(x₁) = f(x₂)= |f(x3)= c. Calculate the approximate value of the integral using the midpoint rule. Area d. Calculate the approximate value of the integral using Simpson's rule. Area e. It is possible to show that an antiderivative of x e-*/3 is −3(x+3) e-3 Using this antiderivative, calculate the exact value of the integral. Integral =
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