Mathematics, 08.02.2022 14:00 BLASIANNkidd
Find the volume, V, of the solid obtained by rotating the bounded region in the first quadrant enclosed by the graphs of
y=x^2, x=y^4
about the x-axis.
Answers: 1
is given by ![\pi \int_a^b [f(x)]^2dx](/tpl/images/2649/6773/9edae.png)
, in our case the volume is given by the expression![\pi [\int_0^1 (\sqrt[4]{x})^2-(x^2)^2 dx] = \pi[\int_0^1 \sqrt{x}-x^4 dx] = \pi[\frac23x^\frac32 -\frac15 x^5 ] _0^1 = \pi (\frac23 -\frac15) = \frac7{15}\pi](/tpl/images/2649/6773/375be.png)
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Find the volume, V, of the solid obtained by rotating the bounded region in the first quadrant enclo...
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