Answer
$g'(x)=x^2$
Work Step by Step
a) Using FTOC 1, $\frac{d}{dx}\int_1^xt^2dt=x^2$
b) $\int_1^xt^2dt=[\frac{t^3}{3}]_1^x=\frac{x^3}{3}-\frac{1}{3}=\frac{1}{3}(x^3-1)$
$\Big(\frac{1}{3}(x^3-1)\Big)'=x^2$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 5 - Section 5.3 - The Fundamental Theorem of Calculus - 5.3 Exercises - Page 399: 5
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