How to Master All the Properties of Definite Integrals
TL;DR: Definite integrals come with a small toolkit of properties that save you a lot of time. You have linearity (constants and sums pull through), additivity over intervals (split a long integral into shorter ones), reversal of bounds (swap the limits, flip the sign), and zero-width intervals (which are simply zero). Knowing these lets you […]
Long Division: How to Deconstruct complex Integrals
TL;DR: If you ever face a rational function where the numerator’s degree is at least as big as the denominator’s, don’t jump straight to fancy techniques. Do polynomial long division first. The result splits into a plain polynomial plus a proper fraction, and each piece is easy to integrate on its own. It is the […]
