Vault Of Euclid

Area Under a Cubic Curve Using Double Integrals

Multiple integrals warmup

Find the area of a region bounded above by the curve \(y = x^3\) and below by \(y = 0\) over the interval \([0, 3]\).
calculus-iiimultiple-integralsdouble-integralarea-using-double-integralsiterated-integralpolynomial-integrationdefinite-integralevaluate-areapower-rulefundamental-theorem-of-calculustype-i-regionintegration-bounds

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What this problem tests

Tests the ability to set up and evaluate a basic double integral over a Type I region.

This problem serves as an introductory example in multivariable calculus for using double integrals to compute areas of 2D regions.

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