Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 4 - Integrals - 4.3 The Fundamental Theorem of Calculus - 4.3 Exercises: 23

Answer

$\frac{52}{3}$

Work Step by Step

Evaluate the integral: $\int^9_1 (\sqrt x) dx$ Recall the 2nd part of the Fundamental Theorem of Calculus: $\int_a^bf(x)dx = F(b) - F(a)$ Find $F(x)$: $F(x) =\int^9_1 (\sqrt x) dx$ $F(x) =\int^9_1 x^{\frac{1}{2} }$ $F(x) = \frac{2}{3}x^{\frac{3}{2} }$ $F(x) =\frac{2\sqrt {x}^3 }{3}$ Now evaluate $F(b) - F(a)$: $F(9) - F(1)$ $\frac{2\sqrt {9}^3 }{3}-\frac{2\sqrt {1}^3 }{3}$ $\frac{2(27) }{3} - \frac{2}{3}$ $\frac{54}{3} -\frac{2}{3} = \frac{52}{3}$
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