Challenging Definite Integral with Square Roots and Logarithms

In summary, the conversation discusses the evaluation of an integral involving a square root and natural logarithms. The individual has been struggling with solving it and has even used Wolfram Alpha for assistance. They mention the properties of logs but are still unsure how to proceed due to the square roots surrounding the logarithmic terms.
  • #1
lordy2010
6
0

Homework Statement



Evaluate integral from -1 to 1 of: sqrt(ln(6-x))/(sqrt(ln(6-x))+sqrt(ln(6+x)))

Homework Equations



n/a

The Attempt at a Solution



I barely know how to approach this integral. I've been trying to figure this out for a long time now, and I feel like I haven't gotten anywhere. I have even used Wolfram Alpha to take a look at the function and it looks like a straight line between -1 and 1. The answer is also, apparently, 1.

Thank you in advanced for the help!
 
Last edited:
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  • #2
Think about using the properties of logs:

ln(xy)=ln(x)+ln(y)
ln(x/y)=ln(x)-ln(y)
 
  • #3
I have considered the properties of logs and, if there were no square roots surrounding each of the ln terms, then I would have an idea of what to do. Unfortunately, there are the square roots outside of the logs so I'm still pretty lost with this integral. :-/
 

What is a tricky definite integral?

A tricky definite integral is an integral that is difficult to solve using traditional methods or techniques. It often involves complex functions or limits of integration that are not easily evaluated.

What are some common techniques for solving tricky definite integrals?

Some common techniques for solving tricky definite integrals include substitution, integration by parts, partial fractions, and trigonometric identities. These techniques can help simplify the integral or manipulate it into a form that is easier to solve.

How can I recognize a tricky definite integral?

A tricky definite integral can often be recognized by the complexity of the integrand, the limits of integration, or the presence of certain functions such as trigonometric, exponential, or logarithmic functions. It may also involve unusual or unconventional techniques for solving.

What are some challenges of solving tricky definite integrals?

Solving tricky definite integrals can be challenging due to the need for advanced mathematical knowledge and skills, as well as the potential for making mistakes during the solution process. It may also require creative thinking and problem-solving abilities to find a suitable approach for solving the integral.

Are there any tips for solving tricky definite integrals?

Some tips for solving tricky definite integrals include breaking down the integral into smaller parts, using symmetry to simplify the integral, and trying multiple approaches if one method does not work. It is also important to check the solution for correctness and to practice regularly to improve problem-solving skills.

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