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education/math/MATH1220 (calc II)/Integral Review.md
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@ -9,4 +9,8 @@ Define $$\int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i=1}^nf(x_i)\Delta x$$
- $\Delta x$ refers to the width of each sub-interval - $\Delta x$ refers to the width of each sub-interval
- $f(x_i)$ refers to the height of each subinterval. - $f(x_i)$ refers to the height of each subinterval.
Then let $f$ be a continous function on $[a, b]$ and let $F$ be the any derivative of $f$ (i.e ) Then let $f$ be a continous function on $[a, b]$ and let $F$ be the antiderivative of $f$ (i.e $F'(x) = f(x)$).
Then $\int_a^b f(x) dx = F(b) - F(a)$.
## Examples
$$ \int_0^1 x^2 dx = \frac{1}{3} x^3 \Big |_0^1 = 1/3(1^3)- 1/3 (0)^3 = 1/3$$