Volume of revolution at line x=-4

In summary, the volume of revolution at line x=-4 refers to the volume of a solid generated by rotating a two-dimensional shape around the vertical line x=-4. It is calculated using the formula V = &pi;∫<sub>a</sub><sup>b</sup>(f(x))<sup>2</sup> dx and has various applications in engineering, physics, and mathematics. It differs from other volume calculations as it involves rotation around a specific line and cannot have negative values.
  • #1
~Sam~
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Homework Statement



Find the volume of the solid obtained by rotating the region bounded by the curves y=0,y=sin(6x),x=6,x=0 about the axis x=−4.


Homework Equations



cylindrical method? circumference*thickness*height


The Attempt at a Solution



So I'm not sure how to write the integral when it rotates along the line x=-4 ..would it be like 2*pi*(-4+x)dx*sin(6x)? or 2*pi*(4-x)dx*sin(6x)? Or something completely different?
 
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  • #2
Nevermind..I got it!
 

FAQ: Volume of revolution at line x=-4

What is the definition of "Volume of revolution at line x=-4"?

The volume of revolution at line x=-4 refers to the volume of a solid generated by rotating a two-dimensional shape around the vertical line x=-4.

How is the volume of revolution at line x=-4 calculated?

The volume of revolution at line x=-4 is calculated using the formula V = π∫ab(f(x))2 dx, where a and b are the limits of integration and f(x) is the function that defines the two-dimensional shape.

What are the applications of calculating the volume of revolution at line x=-4?

The volume of revolution at line x=-4 has various applications in fields such as engineering, physics, and mathematics. It can help in calculating the volume of objects with complex shapes, such as bottles, pipes, and cones.

How does the volume of revolution at line x=-4 differ from other volume calculations?

The volume of revolution at line x=-4 differs from other volume calculations as it involves rotating a two-dimensional shape around a specific line, rather than a point or axis. It also requires integration and knowledge of calculus.

Can the volume of revolution at line x=-4 be negative?

No, the volume of revolution at line x=-4 cannot be negative. It represents a physical quantity, and therefore, can only have positive values. If the calculated volume is negative, it indicates an error in the calculation or an incorrect input.

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