Question

Calculus Question.

By the way, good to see you around guys. :)

My question is: For evaluating integrals, how should I know if I need to use fundamental theorem of calculus f(b) - (a) or the limit of reimann sum formula (definite integral formula)?

Answer 1

It may depend on your teacher/professor, but usually, when you have learned the Fundamental Theorem of Calculus, it is assumed that it is the better method and you should be using that Theorem unless otherwise specified. So if they wanted you to use riemann sums, then they would specifically say so.

Answer 2

Agreed. Also the Fundamental Theorem of Calculus is much easier and quicker to use than Riemann sums.

Answer 3

you will never be able to compute a sum, except in the simplest examples

Answer 4

^ that's a good point! Unless you're working with straight lines (which you're not in calculus), riemann sums are almost always estimates and not accurate values.
While with the theorem, you're working with the variables and the answer you get would be more accurate :)

Answer 5

Riemann Sums is one of the approaches we use to understanding definite integrals. The accuracy of your estimate of the area under a given curve from one x-value a to the ending x-value b is dependent upon the number (n) of approximating rectangles.

In the limit, as the number (n) of approximating rectanges goes to infinity, your Riemann Sum will indeed produce an exact area.

You'll not likely be told to choose one method over the other. You'll learn Riemann Sums first, master this approach, and then move on to definite integrals.