Revolving Volume of R on x=3 using Shell Method

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In summary, the conversation discusses finding the volume of R when it is revolving on x=3 using the shell method. The area of R is equal to 2 m^2 and the volume is equal to 4pi m^3 when it's revolving on Y. The formula used is V_{x=3} = 2pi \int_1^3 (3-x) \cdot f(x) \, dx and the final answer is found.
  • #1
jaychay
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If the area of R is equal to 2 m^2 and the volume of R is equal to 4pi m^3 when it's revolving on Y by using shell method. Find the volume of R when it's revolving on x=3 ?

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Can you please help me ?
I have tried to do it many times but still got the wrong answer.
Thank you in advance.
 
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  • #2
$\displaystyle R = \int_1^3 f(x) \, dx = 2m^2$

$\displaystyle V_{x=0} = 2\pi \int_1^3 x \cdot f(x) \, dx = 4\pi m^3$

$\displaystyle V_{x=3} = 2\pi \int_1^3 (3-x) \cdot f(x) \, dx = \, ?$
 
  • #3
skeeter said:
$\displaystyle R = \int_1^3 f(x) \, dx = 2m^2$

$\displaystyle V_{x=0} = 2\pi \int_1^3 x \cdot f(x) \, dx = 4\pi m^3$

$\displaystyle V_{x=3} = 2\pi \int_1^3 (3-x) \cdot f(x) \, dx = \, ?$
Thank you very much.
I finally find the answer.
 
Last edited:

FAQ: Revolving Volume of R on x=3 using Shell Method

What does "finding the area under the curve" mean?

Finding the area under the curve refers to the process of calculating the total area that is contained within a curve on a graph. This is typically done by using mathematical methods such as integration.

Why is it important to find the area under the curve?

Finding the area under the curve is important in various fields of science, such as physics, engineering, and economics. It allows us to calculate important quantities, such as displacement, work, and profit, which are crucial in understanding and analyzing real-world phenomena.

What is the difference between finding the area under the curve and finding the area of a shape?

While finding the area of a shape involves calculating the total space that is enclosed by the shape's boundaries, finding the area under the curve involves calculating the total space that is contained within a curve on a graph. This often requires the use of more advanced mathematical techniques, such as integration.

How is the area under the curve calculated?

The area under the curve is typically calculated using integration, which is a mathematical process of finding the area under a curve by dividing it into small, infinitesimal rectangles and summing up their areas. This can be done using various integration techniques, such as the Riemann sum or the trapezoidal rule.

Can the area under the curve be negative?

Yes, the area under the curve can be negative. This can occur when the curve dips below the x-axis, resulting in a negative area. In some cases, the area under the curve may also represent the net change in a quantity, which can be positive or negative depending on the direction of the change.

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