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Find the volume of the solid obtained by rotating the region bounded by y = 8x + 40, y = 0, x = 0 about the y-axis. Volume = 136pi/3

User Hitzi
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Final answer:

To find the volume of the solid obtained by rotating the region bounded by y = 8x + 40, y = 0, x = 0 about the y-axis, use the method of cylindrical shells and integrate the function.

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by y = 8x + 40, y = 0, x = 0 about the y-axis, we can use the method of cylindrical shells.

The volume of the solid is given by the integral V = ∫[a, b] (2πx)(8x + 40) dx.

Simplifying that integral gives V = 16π∫[a, b] (x^2 + 5x) dx.

Integrating the function gives V = 16π[x^3/3 + (5/2)x^2], evaluated from x = 0 to x = b.

Substituting the given values into the equation and evaluating the integral gives the desired volume: Volume = (136π/3) cubic units.

User HexYeah
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