Answer to Question #96071 in Calculus for Rachel

Question

A comparison between the Darboux-integral and the Riemann-integral.

Answer 1

We use Darboux - integral (or) Riemann - integral, to approximate the area under curve using limit infimum and limit supremum.

A function is Darboux - integral, if it is Riemann - integral.

In Riemann - integrals, we partition the given interval then we can do the integrations.

In Darboux - integral, we create the rectangle on the basis of the x-axis.

If the function is integrable, the values of Darboux - integral and Riemann - integral are equal.