WEEK #13

This week was a busy learning one. We had off on monday, and a limits test on Tuesday. On Wednesday. We learned about intergration and about LRAM, RRAM, MRAM, and Trapezoidal to find the Riemann sums (approximation of area under a curve using rectangles or trapezoids. Friday we learned about the "real" integration. An integration, denoted by the S looking symbol, is basically looking at f '(x) and finding f(x).

There are two types of Integration: Indefinite and Definite.
Indefinite - answer is an equation.
Definite - answer is a number.

For indefinite: all the same properties of derivativtes apply, just backwards.

For indefinite polynomials: S(x^n)dx = [x^(n+1)]/[n+1] +C.

Example: S(2x^2)dx = 2(x^3/3) +c = (2/3)x^3 +C.

For other indefinites: basically just do the reverse of derivatives.

Example: S(sinx)dx = -cosx +C

You can also rewrite functions to make your life easier.

Example: S(1/x^3)dx can also be written as S(x^-3).

Definite integration:
it is the area formula on an interval [a,b]
aSb (f(x))dx = F(b) - F(a) = A NUMBER

Example:
3S0 (x^2)dx = (1/2)x^3 (30) = (1/3)(3)^3 - 1/2(0)^3 = 9