If x 2-1, let A(x) = (t2+1)dt -1 a. A(x) represents the area of a region. Sketch that region. b. Using the limit of a Riemann Sum, find an expression for A(x). c Using your expression from (b) find dA and simplify. What do you notice?
If x 2-1, let A(x) = (t2+1)dt -1 a. A(x) represents the area of a region. Sketch that region. b. Using the limit of a Riemann Sum, find an expression for A(x). c Using your expression from (b) find dA and simplify. What do you notice?
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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answer a, b and c
Transcribed Image Text:If x 2-1, let
A(x) =
+ 1)dt
a. A(x) represents the area of a region. Sketch that region.
b. Using the limit of a Riemann Sum, find an expression for A(x).
c Using your expression from (b) find
d. If x 2-1 and h is a small positive number, then A(x + h)- A(x) represents the area
of a region. Describe and sketch the region.
Draw a rectangle that approximates the region in part (d). Use this illustration to
demonstrate why for small values of h the following approximation can be used.
and simplify. What do you notice?
e.
A(x +h)-A(x)
*x² + 1
f. Use part (e) to give an intuitive explanation for the result of (c).
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