Differential -OR- Integral Calculus; which is a tougher course?

Question

I'm currently taking calc-I; the purpose of the question is to figure out if calc-II is going to be easier or harder.

Answer 1

Integral calculus. With differential calculus, all of the "ordinary" functions (by which I mean all the field operations, powers, roots, exponential, logarithmic, and trigonometric functions) not only have simple derivatives, but these derivatives may be found by the unthinking application of the product and chain rules. Further, finding a derivative from first principles is a simple task requiring no special insight beyond an understanding of limits. (Of course, for the first time student, "an understanding of limits" is not nearly as trivial as I just made it sound).

Conversely, evaluating integrals requires learning how to take antiderivatives, for which the only rote procedure (the Risch algorithm) is generally considered much to complicated to be taught. Finding integrals in practice therefore requires a considerable degree of insight and understanding, as well as some trial and error. In many cases, a simple-looking function has no elementary antiderivative to find (e^(x²) for instance), and others are themselves extremely simple, but have horrendously complicated antiderivatives (√(tan x) being a very good example of this). And of course, finding antiderivatives at all requires prior mastery of differential calculus.

Answer 2

Integral Calculus is by far harder than differential Calculus, particularly because there's a direct formula for finding the derivative:

lim [f(x + h) - f(x)]/h
h -> 0

For integration, on the other hand, there *is* no direct formula. There are methods to integrate to simulate going "backwards" from the derivative formula, and that's about it. There's also the fact that integral calculus *uses* differential Calculus (such as when using substitution, and the arclength).

Answer 3

it sounds very related to each other, but I guess people would say Integral because integrals follow from derivatives and differentials

*If it's the system where you have Calc I,II, and III, then Calc II is slightly tougher than I, but tCalc III is almost on the level of Calc I.

Answer 4

Accordingly, Integral is a little bit difficult course. Becoz there are lots of branches in Integral calculus. For simplicity, you can use the book: Calculus(7th Edition) by Howard Anton.

Answer 5

I agree with a previous answer. Just about anything you need to know about differentiation can be summarised on one piece of paper. On the other hand, whole books have been written about how to integrate just certain types of functions.

Are they really alternatives for you? You cannot hope to study integration until you are thoroughly familiar with differentiation. Hope that this helps .

Answer 6

Integral is hard unless you are going to use it for spherical needs.... I would prefer Differential because it is easier

Answer 7

There just opposite sides of the same subject. And either one of them is only as difficult as you make it.


Douog