The area bounded by y2=4x and the line x=4 is revolved about the line x=4. Find the
volume of the solid of revolution.
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Answered by
15
Answer:
Parabola y^2 = 4x and the line y = x
The intersection points are x=0 and x=4 by solving the two equations
The volume generated
=∫πy2^2 dx- ∫πy1^2 dx for range x=0 to 4
=∫π(4x)dx- ∫π(x)^2 dx for range x=0 to 4
=4 π x^2/2- π(x)^3/3
=4 π 4^2/2- π(4)^3/3
=32π-64π/3=32π/3
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Answered by
10
Answer:
y^2 = 4x and the line y = x
The intersection points are x=0 and x=4 by solving the two equations
The volume generated
=∫πy2^2 dx- ∫πy1^2 dx for range x=0 to 4
=∫π(4x)dx- ∫π(x)^2 dx for range x=0 to 4
=4 π x^2/2- π(x)^3/3
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=4 π 4^2/2- π(4)^3/3
=32π-64π/3=32π/3
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