Area of y = 2 Sqrt x is rotated about the y axis with attempt

  • Thread starter Riazy
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In summary, a user is seeking help with a problem involving completing the square and integration. They have provided a link to an image file with their progress so far. Another user suggests using the substitution w = a\cosh(t) and asks for the value of a. The original user clarifies that a = 1/2.
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  • #2
Anyone? The information is presented on the uploaded jpg.
 
  • #3
Write
[tex]x^2+x = (x^2+x + 1/4)-1/4=\left(x+\frac 1 2\right)^2-\left(\frac 1 2\right)^2[/tex]

Letting w = x + 1/2 gets it into the form

[tex]\sqrt{w^2-a^2}[/tex]

Then try the substitution [itex]w = a\cosh(t)[/itex]
 
  • #4
What is a in your case?
 
  • #5
Riazy said:
What is a in your case?

You mean in your case. a = 1/2.
 

Related to Area of y = 2 Sqrt x is rotated about the y axis with attempt

1. What is the formula for finding the area of a function rotated about the y-axis?

The formula for finding the area of a function rotated about the y-axis is π∫(y)^2 dx.

2. How do you know when to use the formula for finding the area of a function rotated about the y-axis?

You should use the formula for finding the area of a function rotated about the y-axis when the function is being rotated around the y-axis and the resulting shape is a solid of revolution.

3. Can you provide an example of using the formula for finding the area of a function rotated about the y-axis?

Sure, let's say we have the function y = 2√x and we want to rotate it about the y-axis. The resulting shape will be a solid of revolution and the formula for finding its area would be π∫(2√x)^2 dx.

4. What is the difference between rotating a function about the x-axis and the y-axis?

Rotating a function about the x-axis will result in a shape with a circular cross section, while rotating a function about the y-axis will result in a shape with a cylindrical cross section.

5. Are there any other methods for finding the area of a function rotated about the y-axis?

Yes, there are other methods such as using the disk method or the shell method. These methods involve using different formulas and integrals, but ultimately result in the same area value.

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