Odisea

Andres Fernando tegua perez
Fredy alexander Rincon
Katherine lagos ramos

1.
f(x):=(x^3)/(1+sqrt(x))$
x0:1$
x2:1.5$
x1:(1+1.5)/2$
x3:1.5$
x5:2$
x4:(1.5+2)/2$
h1:x1-x0$
h2:x4-x3$s1:((h1/3)*(f(x0)+(4*(f(x1)))+f(x2)))+((h2/3)*(f(x3)+(4*(f(x4)))+f(x5))),numer;
rta: 1.647099074875294.

2. Simpson.
f(x):=((exp(x))*(sin(%pi*x/180)))/(1+x^2)$
x0:0$
x2:3$
x1:(x2+x0)/2$h1:x1-x0$
s1:((h1/3)*(f(x0)+(4*(f(x1)))+f(x2))),numer;

rta: 0.124754831000214.

sipson 3/8.

f(x):=((exp(x))*(sin(%pi*x/180)))/(1+x^2)$
x0:0$
x1:1$
x2:2$
x3:3$
h1:x1-x0$s1:(((3*h1))*((f(x0))+(3*(f(x1)))+(3*(f(x2)))+(f(x3))))/8,numer;

rta: 0.124126882668884.

3. A. simpson.
f(x):=sin(%pi*x/180)$
x0:0$
x2:pi$
x1:(x2+x0)/2$
h:x1-x0$
s1:((h/3)*(f(x0)+(4*(f(x1)))+f(x2))),numer;rta:2*pi/3.
b. Interpolacion.

x0:0$
x1:90$
x2:180$
y0:0$
y1:1$
y2:0$
g0(h):=((x-x1)*(x-x2))/((h-x1)*(h-x2))$
g1(h):=((x-x0)*(x-x2))/((h-x0)*(h-x2))$
g2(h):=((x-x1)*(x-x0))/((h-x1)*(h-x0))$L0:ratsimp((g0(x0)))$
L1:ratsimp((g1(x1)))$
L2:ratsimp((g2(x2)))$
u:ratsimp((L0*y0)+(L1*y1)+(L2*y2))$
u;
rta: -(x^2-pi*x)/8100

4.

f(x):=2/10+(25*x)-(200*x^2)+(675*x^3)-(900*x^4)+(400*x^5)$
x0:0$
x1:4/15$
x2:8/15$
x3:4/5$
h1:x1-x0$
s1:(((3*h1))*((f(x0))+(3*(f(x1)))+(3*(f(x2)))+(f(x3))))/8,numer;
rta: 1.519170370370373.

5. Polinomio.

x0:0$
x1:1$
x2:2$
x3:3$y0:2$
y1:-2$
y2:-1$
y3:0$
g0(h):=((x-x1)*(x-x2)*(x-x3))/((h-x1)*(h-x2)*(h-x3))$
g1(h):=((x-x0)*(x-x2)*(x-x3))/((h-x0)*(h-x2)*(h-x3))$
g2(h):=((x-x1)*(x-x0)*(x-x3))/((h-x1)*(h-x0)*(h-x3))$g3(h):=((x-x1)*(x-x2)*(x-x0))/((h-x1)*(h-x2)*(h-x0))$
L0:ratsimp((g0(x0)))$
L1:ratsimp((g1(x1)))$
L2:ratsimp((g2(x2)))$
L3:ratsimp((g3(x3)))$
u:ratsimp((L0*y0)+(L1*y1)+(L2*y2)+(L3*y3))$
u;
polinomio…..-(5*x^3-30*x^2+49*x-12)/6.

f(x):=-(5*x^3-30*x^2+49*x-12)/6$
x0:0$
x1:1$
x2:2$
x3:3$

h1:x1-x0$

s1:(((3*h1))*((f(x0))+(3*(f(x1)))+(3*(f(x2)))+(f(x3))))/8,numer;
rta: -2.625.

6.