Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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Transcribed Image Text:This question has several parts that must be completed sequentially. If you skip a part of the question, you will nc
skipped part.
Tutorial Exercise
Evaluate the indefinite integral.
x2
dx
1 + x6
Step 1
We must decide what to choose for u. If u = f(x), then du = f '(x) dx, and so it is helpful to look for some
x2
1 + x6
expression in
dx for which the derivative is also present, though perhaps missing a constant
factor.
Finding u in this integral is a little trickier than in some others.
which is not
We see that 1+ x° is part of this integral, but the derivative of 1 + x° is
present in the integrand.
However, notice that the x in the numerator is close to the derivative of x, which is
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