Trabalho De Calculo Numerico - Integral

1- a)

>>syms x

>>int (x*sin(x))

ans =

sin(x) - x*cos(x)

b)

>>int(x*sin(x),-3,3)

ans =

2*sin(3) - 6*cos(3)

c)

>> x=-3:0.5:3;

>> y=x.*sin(x);

>>trapz(x,y)

ans =

6.1039

d)

>>format long

>>quad('x.*sin(x)',-3,3,10^-3)

ans =

6.222072998887778

2- a)

>>syms t

>>int(t*exp(4*t))

ans =

(exp(4*t)*(4*t - 1))/16

b)

>>int(t*exp(4*t),-3,3)

ans =

(exp(-12)*(11*exp(24) + 13))/16

c)

>> t=-3:0.5:3;

>> y=t.*exp(4.*t);

>>trapz(t,y)

ans =

1.529118064814388e+05

d)

>>format long

>>quad('t.*exp(4.*t)',-3,3,10^-3)

ans =

1.118939191957488e+05

3- a)

>>syms x

>>int((cos(x))^3)

ans =

sin(x) - sin(x)^3/3

b)

>>int((cos(x))^3,-3,3)

ans =

(3*sin(3))/2 + sin(9)/6

c)

>> x=-3:0.5:3;

>> y=(cos(x)).^3;

>>trapz(x,y)

ans =

0.262548871568820

d)

>>format long

>>quad('(cos(x)).^3',-3,3,10^-3)

ans =

0.281018797868466

4- a)

>>syms x

>>int((1-x)*exp(x))

ans =

-exp(x)*(x - 2)

b)

>>int((1-x)*exp(x),-3,3)

ans =

- 5*exp(-3) - exp(3)

c)

>> x=-3:0.5:3;

>> y=(1-x).*exp(x);

>>trapz(x,y)

ans =

-21.584280054540187

d)

>>format long

>>quad('(1-x).*exp(x)',-3,3,10^-3)

ans =

-20.334559618171287