Example: Make up an integral that can be found using the given u-substitution. Then find the indefinite integral. (a) u = x² + 9 (b) u = e"

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 30EQ
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Example: Make up an integral that can be found using the given u-substitution. Then
find the indefinite integral.
(a) u = x2 + 9
(Б) и — е?
For example, if we are given u =
1
. I would write an integral having u and du present.
du
dr.
= -
x2
(E)
cos
Thus, the integral
dx would work.
x2
cos() dr =
cos u
(-а* du) —D f — cos u du 3 —
- sin u + C = – sir
x2
x2
Transcribed Image Text:Example: Make up an integral that can be found using the given u-substitution. Then find the indefinite integral. (a) u = x2 + 9 (Б) и — е? For example, if we are given u = 1 . I would write an integral having u and du present. du dr. = - x2 (E) cos Thus, the integral dx would work. x2 cos() dr = cos u (-а* du) —D f — cos u du 3 — - sin u + C = – sir x2 x2
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