Use differentiation to verify the integration formulas

In summary, the conversation is about using differentiation to verify an integration formula. The formula being verified is the integral of dx/((cx+a)(dx+b))=1/(ad-bc)lnabs((dx+b)/cx+a)) + C. The person has made progress in their verification, but is unsure of how to proceed from their current step. They are advised to use the formula F = ln{f(x)/g(x)} and its derivative to continue with their verification.
  • #1
ranger1716
18
0
ok, so my problem goes like this:

I have that the integral of dx/((cx+a)(dx+b))=1/(ad-bc)lnabs((dx+b)/cx+a)) + C
I have to use differentiation to verify the integration formulas.

So far I've gotten to:

D(1/(ad-bc)lnabs((dx+b)/cx+a)))=(1/ad-bc)((cx=a)/(dx+b)) => (cx+a)/((ad-bc)(dx+b))

where do I go from here to get back to the original integration formula? :confused:
 
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  • #2
You differentiation is at fault.

if you have F = ln{f(x)/g(x)}, then

F = lnf(x) - lng(x)

dF/dx = f'/f - g'/g

where f' = df/dx, g' = dg/dx
 

1. What is differentiation and integration?

Differentiation is a mathematical process of finding the derivative of a function, which represents the rate of change of the function at any given point. Integration, on the other hand, is the reverse process of differentiation and involves finding the area under a curve.

2. How can differentiation be used to verify integration formulas?

By taking the derivative of an integrated function, we can verify if the result matches the original function. If it does, then the integration formula is correct.

3. Why is it important to verify integration formulas?

Verifying integration formulas is important because it ensures the accuracy of our calculations. If the formulas are incorrect, it can lead to errors in mathematical models and real-life applications.

4. Can differentiation be applied to all integration formulas?

Yes, differentiation can be applied to all integration formulas as it is a fundamental mathematical process that can be used to verify the accuracy of any integration formula.

5. Are there any limitations to using differentiation to verify integration formulas?

While differentiation is a powerful tool for verifying integration formulas, it may not always be feasible to use it in every situation. Some integration formulas may be too complex to differentiate or may require advanced techniques.

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