How to find int_0^1 (x^3 + 2ax^2)/(2+x)dx where a is constant

Thread starter sara_87
Start date Feb 1, 2010
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In summary, the purpose of finding this integral is to evaluate the area under the given function between the limits of 0 and 1. This can help in understanding the behavior and properties of the function. To solve this integral, you can use the method of substitution by letting u = 2 + x. Then, you can use the power rule and the rules of integration to evaluate the integral. The constant a does not affect the process of solving the integral, but it does affect the value of the integral. The value of a can change the shape and behavior of the function, which in turn can affect the area under the curve. The method of substitution and the power rule are commonly used to solve this type of integral. You can also

Feb 1, 2010

sara_87

Homework Statement

integrate

[tex]\int_0^1 \frac{x^3+2ax^2}{2+x}[/tex]

where a is constant

Homework Equations

The Attempt at a Solution

I haven't a clue how to start . can someone give me a hint please?

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Feb 1, 2010

Mark44

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Insights Author

Divide x³ + 2ax² by x + 2. You'll get a quadratic polynomial + constant/(x + 2).

FAQ: How to find int_0^1 (x^3 + 2ax^2)/(2+x)dx where a is constant

What is the purpose of finding this integral?

The purpose of finding this integral is to evaluate the area under the given function between the limits of 0 and 1. This can help in understanding the behavior and properties of the function.

How do I approach solving this integral?

To solve this integral, you can use the method of substitution by letting u = 2 + x. Then, you can use the power rule and the rules of integration to evaluate the integral.

What is the significance of a being a constant in this integral?

The constant a does not affect the process of solving the integral, but it does affect the value of the integral. The value of a can change the shape and behavior of the function, which in turn can affect the area under the curve.

Are there any specific techniques or formulas that can be used to solve this integral?

As mentioned before, the method of substitution and the power rule are commonly used to solve this type of integral. You can also use other techniques such as integration by parts or partial fractions, depending on the complexity of the function.

Can this integral be solved analytically or do I need to use numerical methods?

This integral can be solved analytically using the techniques mentioned above. However, if the function is too complex or the limits are not well-defined, numerical methods may be necessary to approximate the value of the integral.