Question

Calcule as seguintes integrais definidas:

Answer 1

Separe na soma e utilize a regra do expoente

$\displaystyle\int_{-1}^33x^2+\dfrac{4}{x^2}dx=\displaystyle\int_{-1}^33x^2dx+\displaystyle\int_{-1}^3\dfrac{4}{x^2}dx=\dfrac{3x^{2+1}}{2+1}|_{-1}^3+\displaystyle\int_{-1}^34x^{-2}=x^3|_{-1}^3+\dfrac{4x^{-2+1}}{-2+1}|_{-1}^3$

$x^3|_{-1}^3-\dfrac{4}{x}|_{-1}^3=\left(3^3-(-1)^3\right)}\right)-\left(\dfrac{4}{3}-\dfrac{4}{(-1)}\right)=27+1-\dfrac{4}{3}-4=\dfrac{68}{3}\\\\ \Rightarrow\displaystyle\int_{-1}^33x^2+\dfrac{4}{x^2}dx=\dfrac{68}{3}$