Give a geometric argument to show that 10 1y20 1 x2 y2 dx dy = 6

Chapter 14, Problem 60

(choose chapter or problem)

Give a geometric argument to show that

$\int_{0}^{1} \int_{0}^{\sqrt{1-y^{2}}} \sqrt{1-x^{2}-y^{2}}\ d x\ d y=\frac{\pi}{6}$

Equation Transcription:

$\int\limits_{0}^{1}\int\limits_{0}^{\sqrt{1-{y}^{2}}}\sqrt{1-{x}^{2}-{y}^{2}}\ dx\ dy=\frac{\pi{}}{6}$

Text Transcription:

integral _0 ^1 integral _0 ^sqrt 1-y^2 sqrt 1-x^2 -y^2 dx dy = pi/6

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