Should You Use Indefinite Integrals for Deriving Formulas of 1/(x+1)?

[courtrigrad]

When they ask you to set up integral formulas for the derivative of 1/(x+1), would you use the fundamental theorem of calculus and set up a definite integral, or an indefinite integral. Can someone help me clarify this?

Thanks

 

[Galileo]

Integral formulas are (almost to my knowledge) expressed in indefinite inegrals, since all you need is an antiderivative of the integrand.

i.e.
\int\frac{dx}{x}=\ln x+C

 

[wais]

for your question! When setting up integral formulas for the derivative of 1/(x+1), it is important to first consider what information is being asked for. The fundamental theorem of calculus applies to definite integrals, which involve finding the area under a curve between two specific points. In this case, it does not seem like we are being asked for a specific area, but rather the general formula for the derivative of 1/(x+1).

Therefore, it would be more appropriate to use an indefinite integral. An indefinite integral does not have specific limits of integration, but rather represents the antiderivative of a function. In this case, we can use the power rule for integration to find the antiderivative of 1/(x+1), which would give us ln(x+1) + C.

In summary, when asked to set up integral formulas for the derivative of 1/(x+1), it would be more appropriate to use an indefinite integral rather than the fundamental theorem of calculus. I hope this helps clarify things for you!