Can't you "confirm" it yourself by differentiating? The derivative of -ln |x|+ ln|x-1|+ cfrasifrasi said:Can anyone confirm that the answer
for int (1/x(x-1))dx
is
- ln|x|+ ln |x-1| + c using partial fractions?
Thank you.
I suspect that is exactly what he did! Doing it again is not a "check".Astronuc said:How about expanding [tex]\frac{1}{x (x-1)}[/tex] into
[tex] \frac{A}{x}\,+\,\frac{B}{x-1}[/tex] and solve for A and B
then solve the integral
Confirming the answer for an integral means to verify that the solution is correct and accurate. This involves checking the steps used to solve the integral and ensuring that they are mathematically sound.
It is important to confirm the answer for an integral because a small mistake in the solution process can lead to an incorrect answer. By confirming the answer, you can catch any errors and ensure the accuracy of the solution.
You can confirm the answer for an integral by solving the integral using a different method, such as using a calculator or computer software. You can also check your solution by differentiating the answer to see if it matches the original integrand.
Yes, the answer for an integral can be confirmed without solving it by using the Fundamental Theorem of Calculus. This theorem states that the derivative of the definite integral of a function is equal to the original function. So, by taking the derivative of the solution, you can check if it matches the original integrand.
If you are unable to confirm the answer for an integral, you should double-check your solution and steps used to solve the integral. It may also be helpful to seek assistance from a tutor or professor. If you are still unable to confirm the answer, you may need to review your understanding of integration techniques and practice more problems.