INTEGRALS
If derivatives break a function down to its instantaneous speed, Integrals build those moments back up to find the Total Accumulation.
Pixels to Smoothness
Finding the area of a square is easy. Finding the area under a curve is hard. Our solution? Chop the curve into rectangles.
As you increase the Resolution (n), the rectangles get thinner. The blocky gaps disappear, and the estimated area becomes the exact area.
This visual-first method of slicing and summing is the heart of integration.
Curriculum
5 ModulesRiemann Sums
Slicing shapes into rectangles to estimate the impossible area under a curve.
The Definite Integral
Applying the limit to Riemann sums to find the exact, perfect area.
Fundamental Theorem
The beautiful proof that connects Derivatives and Integrals as exact opposites.
U-Substitution
A technique to undo the Chain Rule and integrate nested, complex functions.
Integration by Parts
When functions are multiplied together, we use this trick to untangle them.
Notation Decoder
An elongated "S" standing for "Sum". It tells you to add up an infinite number of tiny slices.
f(x)The function you are integrating. In geometry, this represents the height of the rectangles.
dxThe infinitesimally small width of the rectangles. It marks the variable you are integrating with respect to.