In this question, you will estimate the value of the integral c9 [²² using three different approximations. xe-5 da dx a. Subdivide the interval [3,9] into three sub-intervals of equal width and complete the following Ax = 2 ao 3 a₁ = 5 a2 7 f(ao): = 3e f(a₁) = f(a₂) a3 = 9 f(a3) X1 = 4 f(x₁) = X2 = 6 f(x₂)= X3 = 8 f(x3) b. Calculate the approximate value of the integral using the trapezoidal rule. Area 4.7981 c. Calculate the approximate value of the integral using the midpoint rule. Area 4.8438 d Calculate the approximato value of the integral using Simpson's rule II = = = X

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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In this question, you will estimate the value of the integral
c9
[²²
using three different approximations.
xe-* da
a. Subdivide the interval [3,9] into three sub-intervals of equal width and complete the following
Ax = 2
ao
3
a₁ = 5
a2
7
f(ao): = 3e
f(a₁) =
f(a₂)
a3
= 9
f(a3)
X1 = 4
f(x₁) =
X2 = 6
f(x₂)=
X3 = 8
f(x3)
b. Calculate the approximate value of the integral using the trapezoidal rule.
Area
4.7981
c. Calculate the approximate value of the integral using the midpoint rule.
Area
4.8438
d. Calculate the approximate value of the integral using Simpson's rule.
Area 4.457
II
=
=
=
e. It is possible to show that an antiderivative of x e**/3 is
−3 (x+3) e-
333
X
Using this antiderivative, calculate the exact value of the integral.
Integral = 4.8297
Transcribed Image Text:In this question, you will estimate the value of the integral c9 [²² using three different approximations. xe-* da a. Subdivide the interval [3,9] into three sub-intervals of equal width and complete the following Ax = 2 ao 3 a₁ = 5 a2 7 f(ao): = 3e f(a₁) = f(a₂) a3 = 9 f(a3) X1 = 4 f(x₁) = X2 = 6 f(x₂)= X3 = 8 f(x3) b. Calculate the approximate value of the integral using the trapezoidal rule. Area 4.7981 c. Calculate the approximate value of the integral using the midpoint rule. Area 4.8438 d. Calculate the approximate value of the integral using Simpson's rule. Area 4.457 II = = = e. It is possible to show that an antiderivative of x e**/3 is −3 (x+3) e- 333 X Using this antiderivative, calculate the exact value of the integral. Integral = 4.8297
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