Vault Of Euclid

Volume of Revolution Yielding a Logarithm

Logarithmic and exponential functions warmup

Find the volume of the solid obtained by revolving about the \(x\)-axis the region in the first quadrant under \(y = x^{-1/2}\) between \(x = \frac{1}{4}\) and \(x = 1\).
calculus-ivolume-of-revolutiondisk-methoddefinite-integralnatural-logarithmlogarithm-propertiesintegrationsolid-of-revolutionevaluate-integralfind-volume

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What you need first

What this problem tests

Tests the ability to set up a volume integral using the disk method, integrate 1/x, and simplify logarithmic expressions.

This is a standard application of the definite integral in a first-year calculus course.