- how do I evaluate this integral?

  • Thread starter frasifrasi
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In summary, the conversation is about evaluating an integral of sqrt(x)*ln(x) from 1 to 4. The person tried using parts but it didn't work and asked for help. Another person reminded them of the derivative rule and gave the solution as 16/3ln4 - 28/9. The person then asked for clarification on how to arrive at the solution and was told to subtract the exponents, to which they replied with confirmation.
  • #1
frasifrasi
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URGENT - how do I evaluate this integral?

integral from 1 to 4 of sqrt(x)*ln (x) dx

I tried parts but didn't work

Does anyone know?
 
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  • #2
Sure it works!
Remember that [tex]\frac{d}{dx}\frac{2}{3}x^{\frac{3}{2}}=x^{\frac{1}{2}}=\sqrt{x}[/tex]
 
  • #3
The answer is 16/3ln4 - 28/9

WHen i get to int vdu , I have int sqrt(x)*1/x dx, is this right?

Do i just subtract the exponents from here?
 
  • #4
frasifrasi said:
The answer is 16/3ln4 - 28/9

WHen i get to int vdu , I have int sqrt(x)*1/x dx, is this right?

Do i just subtract the exponents from here?

yes...
 

1. What methods can I use to evaluate an integral?

There are several methods that can be used to evaluate an integral, including substitution, integration by parts, partial fractions, and trigonometric substitution. The most appropriate method to use will depend on the specific integral that you are trying to evaluate.

2. How do I know which method to use for a specific integral?

The best way to determine which method to use is to look for patterns in the integral. For example, if the integrand contains a polynomial term, substitution may be a good method to try. If the integrand contains a product of functions, integration by parts may be appropriate. It is also helpful to practice using each method so you can become familiar with their strengths and limitations.

3. Can I use a calculator to evaluate an integral?

Yes, there are several online calculators and software programs that can help you evaluate integrals. However, it is important to note that these tools may not always give the most accurate or complete answer. It is always a good idea to double check your work by hand if possible.

4. Can I use algebra to simplify an integral before evaluating it?

Yes, simplifying the integrand using algebraic techniques such as factoring, expanding, or combining like terms can often make an integral easier to evaluate. This can also help you determine which method to use to evaluate the integral.

5. Are there any tips for evaluating integrals more efficiently?

Some tips for evaluating integrals more efficiently include looking for symmetry in the integrand, using trigonometric identities, and breaking the integral into smaller, more manageable parts. It is also helpful to practice regularly and become familiar with the various techniques for evaluating integrals.

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