What Are the Different Solutions for Integrating xsin^2xdx?

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In summary, a misc integral is a type of integral used to find the area under a curve that is not a definite or indefinite integral. They are important because they allow for a wider range of mathematical problems to be solved, and they are commonly used in complex calculations for more accurate solutions. Solving a misc integral requires knowledge of integration techniques and the properties of integrals. They have real-life applications in physics, engineering, and economics, such as calculating the center of mass or work done by a force. Misc integrals can also have a physical interpretation, such as representing distance traveled or work done.
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[tex]
\int xsin^2xdx
[/tex]
[tex]
\frac{1}{2}\int x(1-cos2x)dx
[/tex]
[tex]
\frac{x^2}{4}-\frac{1}{2}\int xcos2xdx
[/tex]
[tex]
\frac{x^2}{4}-\frac{xsin2x}{4}-\frac{cos2x}{8}+C
[/tex]
 
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Why are you posting? Just for info for other people?
 
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diffrent solutions
 

What is a misc integral?

An integral is a mathematical tool used to find the area under a curve. A misc integral is a type of integral that does not fall under the commonly used types, such as definite or indefinite integrals.

Why is a misc integral important?

Misc integrals are important because they allow us to solve a wider range of mathematical problems. They are often used in more complex calculations and can provide more accurate solutions.

How do you solve a misc integral?

Solving a misc integral involves using various integration techniques, such as substitution, integration by parts, or partial fraction decomposition. It also requires a deep understanding of the properties of integrals and their applications.

What are some real-life applications of misc integrals?

Misc integrals have various applications in physics, engineering, and economics. For example, they can be used to calculate the center of mass of an object, the work done by a force, or the value of a financial derivative.

Can a misc integral have a physical interpretation?

Yes, a misc integral can have a physical interpretation. For example, the integral of a velocity function represents the distance traveled by an object, and the integral of a force function represents the work done by that force.

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