# Visual Integrals for Programmers
Canonical public lesson for integrals.
## One picture
An integral adds up many tiny rectangles under a curve.
## Simple idea
Area can be approximated by slicing it into narrow columns.
```text
total area ≈ sum(height × width)
```
## Programmer view
```python
def approximate_integral(f, start, end, steps):
width = (end - start) / steps
total = 0
for i in range(steps):
x = start + i * width
total += f(x) * width
return total
```
## Why it matters
Integrals model accumulation: area, distance, total cost, stored energy, probability, and quantity over time.
Source task: `a3e71661-caa7-4297-bede-46f800b21593`