Calculating Volume of a Solid Using Integrals

Thread starter bobsmith76
Start date Feb 4, 2012
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Solid Volume

In summary, to find the volume of a solid using integrals, you need to determine the limits of integration and set up the integral using the appropriate formula. The formula for calculating volume using integrals is V = ∫A(x)dx, where A(x) represents the area of the cross-section of the solid at a particular value of x. The limits of integration depend on the shape and orientation of the solid, and integrals can be used to find the volume of irregularly shaped solids. Some real-world applications of calculating volume using integrals include engineering, physics, chemistry, economics, and finance.

Feb 4, 2012

bobsmith76

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I dont' see why you don't take the antiderivative of pix^(1/2) which makes it

(2pix^(3/2))/3

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Feb 4, 2012

jbunniii

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Because the integrand is [itex]\pi [\sqrt{x}]^2[/itex], not [itex]\pi \sqrt{x}[/itex].

Feb 4, 2012

bobsmith76

thanks. my book did a real poor job of explaining that.

Related to Calculating Volume of a Solid Using Integrals

1. How do you find the volume of a solid using integrals?

To find the volume of a solid using integrals, you need to first determine the limits of integration and set up the integral using the appropriate formula. Then, you need to integrate the function with respect to the variable representing the axis of rotation. The resulting value will be the volume of the solid.

2. What is the formula for calculating volume using integrals?

The formula for calculating volume using integrals is V = ∫A(x)dx, where A(x) represents the area of the cross-section of the solid at a particular value of x. This formula is based on the concept of slicing the solid into infinitesimally thin discs and adding up their volume using integration.

3. What are the limits of integration for finding volume using integrals?

The limits of integration for finding volume using integrals depend on the shape and orientation of the solid. For a solid with a circular cross-section, the limits will be the radius of the circle. For a solid with a rectangular cross-section, the limits will be the length and width of the rectangle. It is important to correctly identify the limits for accurate calculation of volume.

4. Can you find the volume of irregularly shaped solids using integrals?

Yes, integrals can be used to find the volume of irregularly shaped solids. To do so, you would need to use the appropriate formula for the cross-sectional area and integrate with respect to the axis of rotation. This method is often used in calculus to find the volume of objects with complex shapes.

5. What are some real-world applications of calculating volume using integrals?

Calculating volume using integrals has many real-world applications. It is used in engineering to design objects with specific volumes, in physics to calculate the volume of objects with irregular shapes, and in chemistry to determine the volume of solutions. It is also used in economics and finance to calculate the volume of goods or assets. Overall, the concept of volume is widely used in many fields, making the use of integrals to calculate it an important tool in various industries.