Answer
$\dfrac{1}{3} (2 \sqrt 2 -1)$
Work Step by Step
The mass of an object can be found as:
$m=\int_a^b \rho(x) \ dx$
This implies that
$m=\int_0^1 (x \sqrt {2-x^2}) \ dx \\=|\dfrac{-(2-x^2)^{3/2}}{3}|_0^1\\=\dfrac{1}{3} (2 \sqrt 2 -1)$
Calculus: Early Transcendentals (2nd Edition)
by Briggs, Bill L.; Cochran, Lyle; Gillett, Bernard
Published by
Pearson
ISBN 10:
0321947347
ISBN 13:
978-0-32194-734-5
Chapter 6 - Applications of Integration - 6.7 Physical Applications - 6.7 Exercises - Page 467: 13
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