Integral Problem: Solving x^2+a^2

orthovector · 2009-02-27T04:32:42+00:00

does anybody know how to take this integral? \int \frac{dx}_{({x^2 + a^2})^{3/2}}

Thread starter orthovector
Start date Feb 26, 2009
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Integral

In summary, an integral problem involves finding the area under a curve in a given interval. This is a fundamental concept in calculus and can be used to solve a variety of real-world problems. x^2+a^2 represents the function we are trying to find the area under, which in this case is a quadratic function with a variable x and a constant a. The power rule of integration can be used to solve this integral problem, which involves increasing the power of the variable by 1 and dividing by the new power. The solution to this problem is (x^3)/3+a^2x+C, where C is the constant of integration and represents all possible solutions. Other methods such as substitution, integration by parts, and partial fractions

Feb 26, 2009

orthovector

does anybody know how to take this integral?

[tex] \int \frac{dx}_{({x^2 + a^2})^{3/2}} [/tex]

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Feb 26, 2009

csprof2000

Not too bad.

Just use a trig substitution. let x = a tan Q, and then it works out nicely.

Feb 27, 2009

orthovector

well, look at that...!

thanks!

1. What is an integral problem?

An integral problem involves finding the area under a curve in a given interval. It is a fundamental concept in calculus and is used to solve a variety of real-world problems.

2. What is x^2+a^2 in the integral problem?

x^2+a^2 represents the function we are trying to find the area under. In this case, it is a quadratic function with a variable x and a constant a.

3. How do you solve the integral problem x^2+a^2?

To solve this integral problem, you would use the power rule of integration. This involves increasing the power of the variable by 1 and dividing by the new power. In this case, you would get (x^3)/3+a^2x+C as your solution.

4. What is the significance of the constant C in the solution?

The constant C is known as the constant of integration and represents all possible solutions to the integral problem. It is added at the end of the solution as it could have any value.

5. Can the integral problem x^2+a^2 be solved using other methods?

Yes, there are other methods to solve this integral problem such as substitution, integration by parts, and partial fractions. These methods may be more efficient for certain types of functions.