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Find the volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis

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shubhamchouhanvrVT

The volume of the solid generated by revolving the region bounded by the given curve and lines y = 2x, y = 2, x = 0 about the x-axis will be  

V = 8π/3

What is volume integration?

When the integration is done in the three dimensions in the three coordinates x,y and z then we will call it as a volume integration.

I set y=2x = y=2 to find where the intersect each others so I can have my boundaries for integration.

You goal is to find the area so you can integrate around that area. We're revolving around the x-axis so the area will be a circle.

V = ∫A(x)dx =  ∫(πr²)dr

Since we have two different radius, we subtract them from each others.

∫(πr₂² - πr₁²)dr

∫(π(2)² - π(2x)²)dr

∫(4π - 4πx²)dr

4π∫(1 - x²)dr

integrate from 0 to 1 since that's where our boundary is.

V = 4π∫(1 - x²)dr = 8π/3

Hence the volume of the solid generated by revolving the region bounded by the given curve and lines y = 2x, y = 2, x = 0 about the x-axis will be V = 8π/3

To know more about Volume integration follow

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