the new thing that we learned included integration and reiman sums.
we revied limits which was taught at the end of last year/beginning of this year.
REIMAN SUMS:
-an approximation of area using rectangles and trapezoids.
LRAM- left hand approximationx
[f(a) + f(a + x) + … f(b – x)]
RRAM – right hand approximationx
[f(a + x) + … + f(b)]
MRAMx
[f(mid) + f (mid) + …]
Trapezoidal
x/2[f(a) + 2f(a + x) + 2f(a + 2x) + … + f(b)]
INTEGRATION: basically a derivative.. backwards, but there are no quotient rules, product rules, etc.
There are two types of intergation. These two types of integration are indefinite and definite.
Indefinite: the result of indefinite integration is an equation.
Definite: the result of definite integration is a number.
as far as limits, that stuff is relatively easy, i just needed a refresher.
Infinite limits:
top degree=the bottom degree
-the answer is the top coefficient over the bottom coefficient.
Ex: lim as x approaches infinity of 3x-1/2x+3
lim=3/2
top degree>bottom degree
-the answer is infinity
top degree
as far as what i dont understan.. everything is relatively easy, it will just take alot of practice to get used to integration. this may be a dumb question/statement but i don't really know where the numbers ontop of the S come from for integration and why sometimes they change within the same problem.
Well, I can't tell you where they come from except out of thin air, but you plug them into the ingegrated function. And they change because they want to know something from x to z and from z to y. :)
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