Question regarding Integral calculus.

Question

In Integral calculus, the condition is that "dx" should approach zero and not become zero, right?

if it becomes zero then there will be no "area of rectangle" to calculate and we would get only the value of y-axis. am i right?

Answer 1

Hi Rahul,

You are right in that dx should approach 0 and not actually be 0. Remember how dx is defined. In Algebra, to denote "change in x" we use Δx. For example, we define slope to be Δy/Δx, or "change in y divided by change in x." In Calculus, we are interested if this "change in x" becomes extremely small, and "Δ" becomes "d" when the change in a variable is infinitesimally small. So, slope (or the derivative) becomes dy/dx.

The algebraic basis for integral calculus is the Riemann Sum, where you sum a lot of rectangles with a height of f(x) (the function) and a width of Δx. If Δx = 0, then all the areas would be just 0 and we would not have an integral. This is why in integral calculus, dx cannot be 0, but approaches 0. The summation becomes an integral and Δx becomes dx, similar to differential calculus.

Hope this helps,

Akshat Y.