integral todo list

[Akuli]

• int_a^b + int_b^c = int_a^c when a<b<c
• same as above with all numbers a,b,c, and how integrals have to be defined for it to work
• integral average
• fundamental theorem of calc part 1, with integral average
• fundamental theorem of calc part 2

antiderivatives and everything related to them:

• notation for F(b)-F(a)
• +C
• integrating f(x)+g(x)
• integrating f(x)-g(x)
• integrating constant*f(x)
  • mention how +C may disappear suddenly with constant=0
• integral of x^n for n != -1
• integral of x^n for n = -1 (remember abs)
• integral of e^x, or more generaly a^x for a > 0
• how to NOT integrate f(x)g(x)
• IBP?
• trig integrals and how they require trig formulas? (classic example: int sin^2(x) dx)
• u sub (classic example: int cos(x) / sin^2(x) dx)
• partial fractions?

physics:

• what falling objects have to do with parabolas