A calculus problem by Jose Sacramento

Calculus Level 3

True or False? ∫ 0 1 ∫ − 1 − y 2 1 − y 2 1 d x d y = ∫ 0 1 ∫ 0 π r d θ d r \large \int_0^1 \int_{-\sqrt{1-y^2}}^{\sqrt{1-y^2}} 1 \, dx \; dy = \int_0^1 \int_0^\pi r \, d\theta \; dr

False True

Jose Sacramento by Jose Sacramento , 66, Portugal

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1 solution

Steven Chase
Dec 15, 2016

They are both half-circles, but the one on the right is the one on the left rotated by 90 degrees.

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