Integrating the Square Root of a Fraction with a Radical

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In summary, 10.08.06 int with radical is a mathematical expression that combines an integer and a radical symbol. It allows for more accurate calculations and is commonly used in fields such as engineering and finance. However, it has limitations such as only being applicable to square roots and not being able to represent negative numbers. To solve for it, the radical must be simplified and the integer and radical components combined. Some real-life applications include finding diagonal lengths and calculating interest rates.
  • #1
karush
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MHB
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5
$\tiny{10.08.06}\\$
$\textsf{Evaluate the function}$
\begin{align*}\displaystyle
I_5&=\int \sqrt{\frac{x^2-4}{x}} \, dx
\end{align*}

ok, I thought this would be a simple U subst, but nothing looks convienent
 
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  • #2
W|A gives a non-elementary result.
 
  • #3
I presume when $x=0$ it is undefined:cool:
 
  • #4
Are you sure you did not mean $\int \frac{\sqrt{x^2-4}}{x}\,\mathrm{d}x$?
 

FAQ: Integrating the Square Root of a Fraction with a Radical

What is 10.08.06 int with radical?

10.08.06 int with radical is a mathematical expression that involves an integer and a radical (square root) symbol. It represents a number that is a combination of a whole number and a fractional or irrational component.

What is the purpose of using int with radical?

The use of int with radical allows for more precise and accurate calculations when dealing with numbers that are not whole, but cannot be expressed as a decimal. It also allows for easier and more efficient representation of numbers in certain equations and problems.

How does one solve for 10.08.06 int with radical?

To solve for 10.08.06 int with radical, you must first simplify the radical as much as possible. Then, you can combine the integer and radical components to get the final value. In some cases, you may need to use algebraic methods or a calculator to find the exact value.

What are some real-life applications of 10.08.06 int with radical?

Int with radical is commonly used in various fields such as engineering, physics, and finance. For example, it can be used to calculate the length of a diagonal in a right triangle, or to determine the amount of interest earned on an investment with a fixed interest rate. It can also be used in computer programming to generate random numbers within a certain range.

Are there any limitations or restrictions when using int with radical?

Int with radical can only be used for square roots (2nd roots) and not for higher order roots such as cube roots or 4th roots. It also cannot be used for negative numbers, as the square root of a negative number is undefined in the real number system. Additionally, some irrational numbers may not have an exact integer and radical representation, requiring the use of approximations instead.

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