find the integration of x° dx
Answers
Step-by-step explanation:
According to many common definitions of an integral (for example, as the limit of Riemannian sums), the expression ∫xdx is meaningless.
Roughly speaking, an integral is a sum over an infinity of zeros, expressed as the limit of the sum of values of the function times small intervals, as the intervals go to zero in size. In the integral ∫baf(x)dx , the dx represents the small, zero-trending intervals.
One version of this as a sum would be ∫baf(x)dx=limN→∞∑Ni=0f(ai)Δxi where ai=a+iN(b−a),Δxi=1N . There are other versions that work as well. The key being that as the limit goes to infinity, the size of the largest interval, max(Δxi) goes to zero.
The strict interpretation, thereof, of ∫xdx would be the infinite sum of terms which go to infinity, not terms that go to zero. As such, it would be divergent, and wouldn’t exist.