How to Integrate Complicated Volume Integrals of Spheres?

Thread starter geft
Start date Oct 10, 2011
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Integration Sphere Volume

In summary, the formula for finding the volume of a sphere using integration is V = (4/3)πr^3, where r is the radius of the sphere and π is the mathematical constant pi. To set up the integral, we can use the formula V = ∫a^b A(x) dx, where a and b are the limits of integration and A(x) represents the cross-sectional area of the sphere at a given distance x from its center. Any method of integration can be used, but the most common approaches are the disk/washer method and the shell method. The radius of the sphere affects the integration process, as the limits of integration and the formula for the cross-sectional area will change accordingly. Volume integration

Oct 10, 2011

geft

I can't seem to get the answer. How to integrate when it's this complicated?

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Oct 10, 2011

LawrenceC

Assuming correctness up to the next to last line, you can look up the integral of (sinx)**3. The integral of sinx(cosx)**2 is like a**u du because you have du which is sinx * dx.

FAQ: How to Integrate Complicated Volume Integrals of Spheres?

What is the formula for finding the volume of a sphere using integration?

The formula for finding the volume of a sphere using integration is V = (4/3)πr³, where r is the radius of the sphere and π is the mathematical constant pi.

How do you set up the integral for finding the volume of a sphere?

To set up the integral for finding the volume of a sphere, we can use the formula V = ∫_a^b A(x) dx, where a and b are the limits of integration and A(x) represents the cross-sectional area of the sphere at a given distance x from its center.

Can I use any method of integration to find the volume of a sphere?

Yes, any method of integration can be used to find the volume of a sphere. However, the most common approach is to use the disk/washer method or the shell method.

Does the radius of the sphere affect the integration process?

Yes, the radius of the sphere does affect the integration process. As the radius changes, the limits of integration and the formula for the cross-sectional area will also change accordingly.

How can I use volume integration of a sphere in real-life applications?

Volume integration of a sphere can be used in various real-life applications, such as calculating the volume of a water tank, determining the volume of a balloon, or finding the volume of a spherical object in physics or chemistry experiments.