Exercícios de Cálculo Numérico - Questão 1, 2 e 3

// Quest�o 1

// Solu��o exata: tau=integral(a,b) = 2,304e-28*[-1/x]; a integral definida com a=1e-12 e b=4e-12 resulta em 1,728e-16 J

//

tau=simpson(1e-12,4e-12,'9e9*(1.6e-19)**2/x**2')

tau=simpson_comp([1e-12,1.5e-12,2e-12,2.5e-12,3e-12,4e-12],'9e9*(1.6e-19)**2/x**2')

tau=simpson_exat_crescente(1e-12,4e-12,2,'9e9*(1.6e-19)**2/x**2')

tau=simpson_exat_crescente(1e-12,4e-12,4,'9e9*(1.6e-19)**2/x**2')

//

// Quest�o 2

// Solu��o exata: T(t)=1/(b-a)*integral(a,b)= [0,0001 t**5/5]-[0,280 t**3/3]+[25 t]; a solu��o � 15,7 �C

//

a=-12; b=12

T=1/(b-a)*simpson(a,b,'0.001*x**4-0.280*x**2+25')

T=1/(b-a)*simpson_comp_uniforme(a,b,10,'0.001*x**4-0.280*x**2+25')

T=1/(b-a)*simpson_comp_uniforme(a,b,20,'0.001*x**4-0.280*x**2+25')

T=1/(b-a)*simpson_exat_crescente(a,b,2,'0.001*x**4-0.280*x**2+25')

T=1/(b-a)*simpson_exat_crescente(a,b,4,'0.001*x**4-0.280*x**2+25')

// Quest�o 3

// Solu��o exata: dy/dx = 0,795*cos(0,589x); r=12,196; �rea total = 10 per�odos * r * h = 10 * 12,196 * 10 = 1219,6

//

r=simpson(0,10.67,'sqrt(1+(0.795*cos(0.589*x))**2)')

r=simpson_exat_crescente(0,10.67,2,'sqrt(1+(0.795*cos(0.589*x))**2)')

r=simpson_exat_crescente(0,10.67,4,'sqrt(1+(0.795*cos(0.589*x))**2)')

r=simpson_exat_crescente(0,10.67,8,'sqrt(1+(0.795*cos(0.589*x))**2)')