(a) Change variables using the substitution u = =t. Explain why that won't help with solving this integral.

Mathematics For Machine Technology
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Author:Peterson, John.
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Chapter58: Achievement Review—section Five
Section: Chapter Questions
Problem 30AR: Determine dimension x to 3 decimal places.
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(6) Consider the integral
tet dt.
%3D
Transcribed Image Text:(6) Consider the integral tet dt. %3D
(a) Change variables using the substitution u = t. Explain why that won't help with solving this integral.
(b) Now try integration by parts with u =t. Explain why that won't help with solving this integral (in terms
of the functions we are used to).
(c) It turns out that you cannot express that integral in terms of functions you learned so far. So our best
bet is to approximate it using Riemann sums. First, let's try to understand the function we are integrating.
Find the derivative of the function f(t) =te and decide whether this function is increasing or
decreasing on the interval [1, 2].
(d) Use your answer in (b) to find the worst overestimate and the worst underestimate for our integral I
using 6 rectangles of equal base length. What is the average between the worst overestimate and the
worst underestimate?
Transcribed Image Text:(a) Change variables using the substitution u = t. Explain why that won't help with solving this integral. (b) Now try integration by parts with u =t. Explain why that won't help with solving this integral (in terms of the functions we are used to). (c) It turns out that you cannot express that integral in terms of functions you learned so far. So our best bet is to approximate it using Riemann sums. First, let's try to understand the function we are integrating. Find the derivative of the function f(t) =te and decide whether this function is increasing or decreasing on the interval [1, 2]. (d) Use your answer in (b) to find the worst overestimate and the worst underestimate for our integral I using 6 rectangles of equal base length. What is the average between the worst overestimate and the worst underestimate?
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