Question

O VALOR DA INTEGRAL DEFINIDA (X+1)^3 NO INTERVALO DE 1 A 3

Answer 1

$\displaystyle\int_1^3 (x+1)^3\,dx$


Substituição:

$x+1=u~~\Rightarrow~~dx=du$


Mudando os extremos de integração:

$\text{Quando }x=1~~\Rightarrow~~u=2\\\\ \text{Quando }x=3~~\Rightarrow~~u=4$


Substituindo, a integral fica

$=\displaystyle\int_2^4 u^3\,du\\\\\\ =\left.\left(\frac{u^{3+1}}{3+1} \right )\right|_2^4\\\\\\ =\left.\left(\frac{u^4}{4} \right )\right|_2^4\\\\\\ =\frac{4^4}{4}-\frac{2^4}{4}\\\\\\ =\frac{256}{4}-\frac{16}{4}\\\\\\ =\frac{256-16}{4}\\\\\\ =\frac{240}{4}\\\\\\ =60$


Bons estudos! :-)