Surface area of sin(x) rotated about the x-axis

Thread starter emc92
Start date Feb 21, 2012
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Area Surface Surface area

In summary, The formula for finding the surface area of sin(x) rotated about the x-axis is S = 2π∫a^b y√(1 + (dy/dx)^2) dx, where a and b are the bounds of the integral and dy/dx is the derivative of sin(x). Rotating a function about the x-axis means creating a 3-dimensional shape by connecting all points on the original function to the x-axis as it rotates. The amplitude of sin(x) does not affect the surface area when rotated about the x-axis. The method for calculating the surface area is by using the formula and the surface area cannot be negative.

Feb 21, 2012

emc92

got stuck on doing the substitution.. any suggestions?

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Feb 21, 2012

SammyS

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emc92 said:

got stuck on doing the substitution.. any suggestions?

For one thing, the derivative of 1 + cos²(x) is -2sin(x)cos(x), not -2sin(x).

That substitution doesn't seem to help anyway.

Try u = cos(x) instead.

Feb 21, 2012

emc92

wow, i did not see that.
thanks so much!

Related to Surface area of sin(x) rotated about the x-axis

1. What is the formula for finding the surface area of sin(x) rotated about the x-axis?

The formula for finding the surface area of sin(x) rotated about the x-axis is:
S = 2π∫a^b y√(1 + (dy/dx)^2) dx
where a and b are the bounds of the integral and dy/dx is the derivative of sin(x).

2. Can you explain the concept of rotating a function about the x-axis?

Rotating a function about the x-axis means that the function is being rotated around the x-axis, creating a 3-dimensional shape. The resulting shape is formed by connecting all the points on the original function to the x-axis as it rotates.

3. How does the amplitude of sin(x) affect the surface area when rotated about the x-axis?

The amplitude of sin(x) does not affect the surface area when rotated about the x-axis. This is because the rotation only affects the shape of the function, not the distance from the x-axis.

4. Is there a specific method or algorithm for calculating the surface area of sin(x) rotated about the x-axis?

Yes, the method for calculating the surface area of sin(x) rotated about the x-axis is by using the formula mentioned in the first question. This involves finding the derivative of sin(x) and integrating it with respect to x.

5. Can the surface area of sin(x) rotated about the x-axis be negative?

No, the surface area of sin(x) rotated about the x-axis cannot be negative. This is because surface area is always a positive quantity and rotation does not change that. However, the result of the integral may be negative if the bounds of integration are not chosen correctly.