Rounding decimals 324,650
2 answers:
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Trapeoidal rule
know that Δx=(b-a)/n where the endpoints are x=a and x=b and n=number of subintervals
for this one, b=10 and a=0 and n=10 so (10-0)/10=10/10=1
where f(x) is the function and we start at x=a and end at x=b and starting with the term of x₁ and ending with
, the trapezoidal sum is
![\sum\limits^b_a f(x) dx=\frac{\Delta x}{2}[f(x_1)+2f(x_2)...+2f(x_{n-1})+f(x_n)]](https://tex.z-dn.net/?f=%5Csum%5Climits%5Eb_a%20f%28x%29%20dx%3D%5Cfrac%7B%5CDelta%20x%7D%7B2%7D%5Bf%28x_1%29%2B2f%28x_2%29...%2B2f%28x_%7Bn-1%7D%29%2Bf%28x_n%29%5D)
hmm, just minus the sums and if it is negative, multiply by -1
the integral we aproximating is
that is
[0+2(20)+2(35)+2(48)+2(62)+2(75)+2(85)+2(93)+2(99)+2(106)+111]-[0+2(18)+2(31)+2(43)+2(58)+2(68)+2(79)+2(86)+2(93)+2(95)+96]=59.5
B. since it was positive, sappho's car traveled 59mi farther than homer's car
C. average velocity is all the velocities added together
wait, midpoints?
hmm, ok, so we want 5 intervals
so we take average of each section then average them
5 sections
ah, got it
for midpoint, we don't generate our own data
example, from t=0 to t=2, the midpoint value is 20 because it is at t=1
we do the intervals
0 to 2, 2 to 4, 4 to 6, 6 to 8, 8 to 10
midpoints are 20, 48, 75, 93, 106
so we do
(1/5)(20+48+75+93+106)=68.4
the average velocity is 68.4 mph
know that Δx=(b-a)/n where the endpoints are x=a and x=b and n=number of subintervals
for this one, b=10 and a=0 and n=10 so (10-0)/10=10/10=1
where f(x) is the function and we start at x=a and end at x=b and starting with the term of x₁ and ending with
hmm, just minus the sums and if it is negative, multiply by -1
the integral we aproximating is
that is
B. since it was positive, sappho's car traveled 59mi farther than homer's car
C. average velocity is all the velocities added together
wait, midpoints?
hmm, ok, so we want 5 intervals
so we take average of each section then average them
5 sections
ah, got it
for midpoint, we don't generate our own data
example, from t=0 to t=2, the midpoint value is 20 because it is at t=1
we do the intervals
0 to 2, 2 to 4, 4 to 6, 6 to 8, 8 to 10
midpoints are 20, 48, 75, 93, 106
so we do
(1/5)(20+48+75+93+106)=68.4
the average velocity is 68.4 mph