Vault Of Euclid

Changing the Order of Integration for a Triangular Region

Multiple integrals warmup

Changing the order of integration Rewrite the iterated integral \[ \int_{0}^{6} \int_{0}^{x/3} 1 \, dy \, dx \] with the order of integration \(dx \, dy\).
iterated-integralsdouble-integralschanging-order-of-integrationregion-of-integrationmultivariable-calculuscalculus-iiiintegration-boundsreversing-orderlinear-boundstriangular-region

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What this problem tests

Tests the ability to translate algebraic bounds into a geometric region and then re-slice that region in the perpendicular direction.

This is a standard exercise in a multivariable calculus course when introducing double integrals over general regions.

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