What is Integration Really 🌱

\[\int_a^b f(x) dx = \lim_{\Delta x \to 0} \sum_{x=a}^b f(x) \Delta x\] \[\int_{a}^{b} f \left( x \right) dx = \mathop {\lim }\limits_{n \to \infty } \sum\limits_{i = 1}^n f \left( {x_i^*} \right)\Delta x \hspace{0.25in}\hspace{0.25in}\hspace{0.25in} \text{where } \Delta x = \frac{b - a}{n}\]

Integration is just summing the area under a curve. You take the value of the curve at a point (height) and then multiply it by an infinitesimally small increment in the input value (width) and then sum over all these increments.

Notes mentioning this note

There are no notes linking to this note.

Here are all the notes in this garden, along with their links, visualized as a graph.