Question

Resolva a seguinte integral?

$\int\limits^3_2{x/4} \, dx$

Answer 1

Calcular a integral definida

     $\displaystyle\int_2^3 \frac{x}{4}\,dx\\\\\\ =\frac{1}{4}\int_2^3 x\,dx$


Use a regra para integrar potências:

     •   $\displaystyle\int x^n\,dx=\left\{ \!\begin{array}{ll} \dfrac{x^{n+1}}{n+1}+C&\textsf{se~~}n\ne -1\\\\ \ln|x|+C&\textsf{se~~}n=-1 \end{array} \right.$


Aplicando o Teorema Fundamental do Cálculo, a integral fica

     $=\dfrac{1}{4}\cdot \left(\dfrac{x^{1+1}}{1+1}\right)\!\bigg|_2^3\\\\\\ =\dfrac{1}{4}\cdot \left(\dfrac{x^2}{2}\right)\!\bigg|_2^3\\\\\\ =\dfrac{1}{4}\cdot \left(\dfrac{3^2}{2}-\dfrac{2^2}{2}\right)\\\\\\ =\dfrac{1}{4}\cdot \left(\dfrac{9}{2}-\dfrac{4}{2}\right)\\\\\\ =\dfrac{1}{4}\cdot \dfrac{5}{2}$

     $=\dfrac{5}{8}\quad\longleftarrow\quad\textsf{esta \'e a resposta.}$


Bons estudos! :-)