(a) Change variables using the substitution u = =t. Explain why that won't help with solving this integral.
(a) Change variables using the substitution u = =t. Explain why that won't help with solving this integral.
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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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16dc5985-81f4-4a72-a186-48f33283a14f%2Ff1f2fdf7-4f40-4363-9e66-a595e714242e%2F7ay2kcb_processed.jpeg&w=3840&q=75)
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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