The Volume of the solid formed by the curves y = 4x³ , y = 4x, x ≥ 0 ; about the x axis is 64π/21 .
In the question ,
it is given that ,
the given curves are y = 4x³ , y = 4x, x ≥ 0 ,
we have to find the volume about x axis ,
the region formed by the given curves about x axis is shown below in the figure .
So , the Volume of the required region is
V = [tex]\int\limits^1_0 {\pi [(4x)^{2} - (4x^{3} )^{2} }] \, dx[/tex]
On simplification ,
we get ,
V = [tex]\pi \int\limits^1_0 { [16x^{2} - 16x^{6} }] \, dx[/tex]
V = π[ x³/3 - x⁷/7 ]¹₀
= 16π( 1/3 - 1/7 - 0 - 0)
= 16π((7 - 3)/21)
= 64π/21
Therefore , the required Volume is 64π/21 .
The given question is incomplete , the complete question is
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4x³ , y = 4x, x ≥ 0 ; about the x-axis .
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