Second of the Holiday Posts

Hope everybody had a good New Year's...

I'll start with Integration for this post.

Sooo, Integration is the area under a curve, and riemann sums are approxamations of this area using rectangles or trapezoids

You can use LRAM, RRAM, MRAM, or Trapezoidal to do these approxamations.

LRAM is when you start estimating from the left side by drawing rectangles from the x-axis up to the graph and then go over to the right and go down.
Equation form: delta x [f(a) + f(a + delta x) + ... + f(b - delta x)]

RRAM is when you start estimating from the right side by drawing rectangles from the end of the interval of the graph being looked at to where you want to go down with the rectangle.
Equation form: deltax [f(a + delta x) + f(b)]

MRAM is the midpoints and basically a combination of RRAM and LRAM.
Equation form: delta x [f(mid point 1) + f(mid point 2) + f(mid point n + 1)]

Trapezoidal Riemann Sums are the most accurate of the 4 because with the trapezoid, you can get closer to the curve.
Equation form: delta x / 2 [f(a) + 2f(a + delta x) + 2f(a + 2delta x) + ... + f(b)]

Oh, I forgot. A and B are also [a,b], which is the interval the curve is on. Delta x is equal to (b - a) / n.

Well I guess I'll go into the exact integration on the third post. Again, I hope everybody had a nice two weeks off and see you all on Monday. :)