Count On Me (Bruno Mars)

If you ever find yourself stuck in the middle of the sea,

I'll sail the world to find you

If you ever find yourself lost in the dark and you

can't see,

I'll be the light to guide you

Find out what we're made of

What we are called to help our friends in need

You can count on me like one, two, three

I'll be there

And I know when I need it I can count on you like

Four, three, two

And you'll be there

Cause that's what friends are supposed to do,

Oh yeah

Wooooh, wooooh

If you're tossing and you're turning

and you just can't fall asleep

I'll sing a song beside you

And if you ever forget how much you really mean to me

Everyday I will remind you

Oh

Find out what we're made of

When we are called to help our friends in

need.

MatLab® para Engenharia (11)

Resolução de Integrais Indefinidas:

Continuamos a utilização do comando syms, pois ainda estamos utilizando variáveis e expressões simbólicas.

Os passos de resolução de integral é como os de derivada, só que invés de usarmos o comando diff (de derivada), utilizamos o comando int (de integral). Veja como é simples:

>> int(x^3-2*x^2+8)

ans =

(x*(3*x^3 - 8*x^2 + 96))/12

 

>> int(1/x)

ans =

log(x)

 

>> int((x^2)/((x^3-2)^(1/2)))

ans =

(2*(x^3 - 2)^(1/2))/3

 

>> int((exp(cos(x)))*sin(x))

ans =

-exp(cos(x))

 

>> int(coth(2*x))

ans =

log(sinh(2*x))/2

 

>> int(log(x^2))

ans =

x*(log(x^2) - 2)

 

>> int(cos(x)*exp(x))

ans =

(exp(x)*(cos(x) + sin(x)))/2

 

>> int((sinh(2*x))*(exp(x)))

ans =

1/(2*exp(x)) + exp(3*x)/6

 

Integração dupla: Faz-se como em resolução de derivadas de ordem superior:

>> int(int(x^2))

ans =

x^4/12

 

>> int(int(cos(2*x)))

ans =

sin(x)^2/2 - 1/4

 

>> int(int(log(x)))

ans =

(x^2*(2*log(x) - 3))/4