This week in calc we started off by having our limits test which i would have liked to do better on. Then we learned integration which involves Lram Rram Mram and trapezoid. Integration is the are under a curve and you can approximate it with the four i just listed Mram and trapezoid are the most precise out of the four.
LRAM-left hand approximation
x[f(a)+f(a+x)+...f(b)]
RRAM-right hand approximation
x[f(a+x)+...f(b)]
MRAM-midpoint approximation
x[f(mid)+f(mid)+...]
Trapezoid-approximates using a trapezoid
x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]
An example of integration is:
x^2-3 [1,4] n=3
First you find your delta x which is 1
LRAM 1[f(1)+f(2)+f(3)]
1[-2+1+6]
1[5]=5
RRAM 1[f(2)+f(3)+f(4)]
1[1+6+13]=20
MRAM 1,2,3,4
2+1/2=3/2
3+2/2=5/2
4+3/2=7/2
1[-3/4+13/4=37/4]=47/4
Trapezoid
1/2[f(1)+2f(2)+2f(3)+f(4)]
1/2[-2+2+12+13]=25/2
What I have the most trouble with is MRAM and trapezoid. Mram just because i am very bad at fractions and trapezoid becuase i don't really understand how it works and how to find it so if someone can help me with that thanks.
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MRAM is just the midpoints of the numbers on the interval given. Say you are given x^2 + 2 on the interval [0,3] and n= 3
ReplyDeleteyou would have the numbers 0, 1, 2, and 3
then you would take the midpint of each number by adding then dividing by two.
0+1/2 = 1/2
1+2/2 = 3/2
2+3/2= 5/2
after that you just plug into your equation
1[f(1/2) + f(3/2) +f(5/2)]
then solve.
Trapezoidal is the best method to use.
Instead of using delta x you use delta x/ 2
so 1/2 [ f(0) + 2f(1) + 2f(2) +f(3)]
and then plug into your equation.
Trapezoidal will always have one more number than the other three.