Antiderivatives
the indefinite integral of 2x dx
x2 + c
Integral represents
Area/accumulation
FTC connects
derivatives and integrals
Substitution reverses
Chain Rule
Integral meaning
Accumulation
the indefinite integral of x3 dx
x4/4 + C
int_0^2 x2 dx
8/3
Formula
F(b)-F(a)
u in ∫2x e^(x^2)
x2
Derivative meaning
Rate of change
Why +C?
Constants disappear in derivatives
Above axis area
Positive
F'(x) of ∫_0^x f(t)dt
f(x)
du for x2
2x dx
Riemann sum
Approximation
the indefinite integral of 5
5x + C
Below axis area
Negative
Use FTC to avoid
Rectangles
Final step
Back substitute
Limit gives
Exact value
Reverse of derivative
Antiderivative
Equal positive & negative
0
Main idea
Exact accumulation
Purpose
Simplify integrals
Key idea
Total change