Calculando a integral obtêm-se:
Anexos:
Soluções para a tarefa
Respondido por
2
Oi . Usando o método da substituição temos o seguinte procedimento.
![\int\limits^\frac{1}{4}_0 {3e^{4y}} \, dy \ \ \ \boxed{u=4y} \ \ \ \frac{du}{dy}=4 \ \ \ -\ \textgreater \ \boxed{dy= \frac{du}{4}} \\ \\ \int\limits^\frac{1}{4}_0 {3e^{u}} \, \frac{du}{4} \ \ \ \ \ Constantes \ para \ fora \\ \\ \frac{3}{4} \int\limits^\frac{1}{4}_0 {e^{u}} \, du \ \ \ \ \ \ A \ integral \ de\ e^u = e^u \\ \\ \frac{3}{4}[e^{4y}]\ |_0^{ \frac{1}{4} } \\ \\ \frac{3}{4}[e^{4. \frac{1}{4} }-e^{4.0 }] \\ \\ \frac{3}{4}[e-e^0] \\ \\\frac{3}{4}[e-1] \ \ \ \ e=2,718 \ (aprox) \\ \\](https://tex.z-dn.net/?f=+%5Cint%5Climits%5E%5Cfrac%7B1%7D%7B4%7D_0+%7B3e%5E%7B4y%7D%7D+%5C%2C+dy+%5C+%5C+%5C+%5Cboxed%7Bu%3D4y%7D+%5C+%5C+%5C+%5Cfrac%7Bdu%7D%7Bdy%7D%3D4+%5C+%5C+%5C+-%5C+%5Ctextgreater+%5C+%5Cboxed%7Bdy%3D+%5Cfrac%7Bdu%7D%7B4%7D%7D+%5C%5C+%5C%5C+%5Cint%5Climits%5E%5Cfrac%7B1%7D%7B4%7D_0+%7B3e%5E%7Bu%7D%7D+%5C%2C+%5Cfrac%7Bdu%7D%7B4%7D+%5C+%5C+%5C+%5C+%5C+Constantes+%5C+para+%5C+fora+%5C%5C+%5C%5C+%5Cfrac%7B3%7D%7B4%7D+%5Cint%5Climits%5E%5Cfrac%7B1%7D%7B4%7D_0+%7Be%5E%7Bu%7D%7D+%5C%2C+du+%5C+%5C+%5C+%5C+%5C+%5C+A+%5C+integral+%5C+de%5C+e%5Eu+%3D+e%5Eu+%5C%5C+%5C%5C+%5Cfrac%7B3%7D%7B4%7D%5Be%5E%7B4y%7D%5D%5C+%7C_0%5E%7B+%5Cfrac%7B1%7D%7B4%7D+%7D+%5C%5C+%5C%5C+%5Cfrac%7B3%7D%7B4%7D%5Be%5E%7B4.+%5Cfrac%7B1%7D%7B4%7D+%7D-e%5E%7B4.0+%7D%5D+%5C%5C+%5C%5C+%5Cfrac%7B3%7D%7B4%7D%5Be-e%5E0%5D+%5C%5C+%5C%5C%5Cfrac%7B3%7D%7B4%7D%5Be-1%5D+%5C+%5C+%5C+%5C+e%3D2%2C718+%5C+%28aprox%29+%5C%5C+%5C%5C+ "\int\limits^\frac{1}{4}_0 {3e^{4y}} \, dy \ \ \ \boxed{u=4y} \ \ \ \frac{du}{dy}=4 \ \ \ -\ \textgreater \ \boxed{dy= \frac{du}{4}} \\ \\ \int\limits^\frac{1}{4}_0 {3e^{u}} \, \frac{du}{4} \ \ \ \ \ Constantes \ para \ fora \\ \\ \frac{3}{4} \int\limits^\frac{1}{4}_0 {e^{u}} \, du \ \ \ \ \ \ A \ integral \ de\ e^u = e^u \\ \\ \frac{3}{4}[e^{4y}]\ |_0^{ \frac{1}{4} } \\ \\ \frac{3}{4}[e^{4. \frac{1}{4} }-e^{4.0 }] \\ \\ \frac{3}{4}[e-e^0] \\ \\\frac{3}{4}[e-1] \ \ \ \ e=2,718 \ (aprox) \\ \\")
Então:
![\boxed{\int\limits^\frac{1}{4}_0 {3e^{4y}} \, dy = 1,288 (aprox) \ u.a. \ [unidades \ de\ area]}](https://tex.z-dn.net/?f=+%5Cboxed%7B%5Cint%5Climits%5E%5Cfrac%7B1%7D%7B4%7D_0+%7B3e%5E%7B4y%7D%7D+%5C%2C+dy+%3D+1%2C288+%28aprox%29+%5C+u.a.+%5C+%5Bunidades+%5C+de%5C+area%5D%7D "\boxed{\int\limits^\frac{1}{4}_0 {3e^{4y}} \, dy = 1,288 (aprox) \ u.a. \ [unidades \ de\ area]}")
Espero que goste. Comenta depois :)
Então:
Espero que goste. Comenta depois :)
Perguntas interessantes