reflection 2

for my academic detention again :( ha

LRAM-left hand approximation

remember to start with the interval all the way to the left and add delta x until you reach your b interval term and substitute that into the original function. add all of those and multiply by delta x:

Dx [f(x+Dx) + … + f(b-Dx)]

RRAM-right hand approximation

same as LRAM, except you start from the right.

Dx[f(b) + f(b+Dx)…f(a+Dx)

TRAM-trapezoidal approximation

remember that delta x is over two and that you should multiply all of the numbers, except your functions of the intervals, by 2.

Dx[f(a) + 2f(a+Dx) + 2f(a+2Dx) +…f(b)]

MRAM-midpoint approximation

Dx[f(mid) +…]

You find the numbers in the midpoints of by adding delta x from a to b.

TRIG INVERSE FUNCTION FORMULAS:

The trig inverse integration formulas are: sqrt=square root
1. S du/sqrt(a^2-u^2)=-1/sqrt(u)arcsin u/a +C
2. S du/a^2+u^2=1/du(a)arctan u/a +C
3. S du/u sqrt(u^2-a^2)=1/du(a)arcsec lul/a +C