Calculus
Study of continuous change through derivatives and integrals.
Advanced Topics
Techniques of Integration
Integrating More Complex Functions
Not all integrals are straightforward! Sometimes you need special tricks to solve them.
Substitution
Change variables to make the integral easier, like undoing the chain rule in reverse.
Integration by Parts
Used when you have a product of two functions. It's based on the product rule for derivatives.
\[ \int u,dv = uv - \int v,du \]
Partial Fractions
Break complicated fractions into simpler pieces you can integrate.
Why Learn These?
These techniques let you solve a wider range of real-world problems involving areas, volumes, and accumulations.
Key Formula
\[\int u,dv = uv - \int v,du\]
Examples
Using substitution to find \( \int 2x \cos(x^2) dx \).
Integrating \( \int x e^x dx \) by parts.
In a Nutshell
Advanced methods help solve tricky integrals for more complex scenarios.