Answer
$9$
Work Step by Step
Here, we have $\dfrac{dc}{dx}=\dfrac{1}{2 \sqrt x}$
$\dfrac{dc}{dx}=(1/2)x^{-1/2}$
This implies that
$c=\int_0^{x} \dfrac{1}{2} t dt$
or, $[t^{1/2}]_0^{x}=\sqrt x$
Thus, $c(100)-c(1)=\sqrt {100}-\sqrt 1=10-1=9$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises - Page 321: 73
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