Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 7 - Integration - 7.2 Substitution - 7.2 Exercises: 4

Answer

\[ -\dfrac{1}{16}(-4t+1)^4+C\]

Work Step by Step

In order to integrate this function, we have to use an «u» substitution. Choose an u, derivate it: $ u=-4t+1$ $ du = -4 dt$ $ -\dfrac{1}{4}du=dx$ Then and substitute: \[ -\dfrac{1}{4} \int u^3 du \] Then integrate \[ = -\dfrac{1}{16}u^4+C \] And undo the substitution: \[ -\dfrac{1}{16}(-4t+1)^4+C\]
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