Question

In this question, you will estimate the value of the integral ?[0,6] xe^(-x/3) dx using three different approximations. a. Subdivide the interval [0,6] into three sub-intervals of equal width and complete the following: ?x = a0 = | f(a0) = a1 = | f(a1) = a2 = | f(a2) = a3 = | f(a3) = x1 = | f(x1) = x2 = | f(x2) = x3 = | f(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 ? 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^(-x/3) is -3(x + 3) e^(-x/3) Using this antiderivative, calculate the exact value of the integral. Integral =

          In this question, you will estimate the value of the integral
?[0,6] xe^(-x/3) dx
using three different approximations.
a. Subdivide the interval [0,6] into three sub-intervals of equal width and complete the following:
?x =
a0 = | f(a0) =
a1 = | f(a1) =
a2 = | f(a2) =
a3 = | f(a3) =
x1 = | f(x1) =
x2 = | f(x2) =
x3 = | f(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 ?
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^(-x/3) is
-3(x + 3) e^(-x/3)
Using this antiderivative, calculate the exact value of the integral.
Integral =

In this question, you will estimate the value of the integral
?[0,6] xe^(-x/3) dx
using three different approximations.
a. Subdivide the interval [0,6] into three sub-intervals of equal width and complete the following:
?x =
a0 = | f(a0) =
a1 = | f(a1) =
a2 = | f(a2) =
a3 = | f(a3) =
x1 = | f(x1) =
x2 = | f(x2) =
x3 = | f(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 ?
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^(-x/3) is
-3(x + 3) e^(-x/3)
Using this antiderivative, calculate the exact value of the integral.
Integral =

Added by Montserrat B.

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