Question

Determine a(s) área(s) da(s) região(ões) compreendida(s) entre as reta(s) e curva(s) abaixo: y=x²-2 e y=2.

Answer 1

$\displaystyle\mathsf{A_{R}=2.\int\limits_{0}^{\sqrt{2}}(4-[x^2-2])dx} \\\displaystyle\mathsf{ =2\int\limits_{0}^{\sqrt{2}}(6-x^2)dx}=12x-\dfrac{2}{3}x^3\Bigg|_{0}^{\sqrt{2}}$

$\mathsf{A_{R} =12\sqrt{2}-\dfrac{2}{3}.2\sqrt{2}}\\\mathsf{A_{R}=12\sqrt{2}-\dfrac{4}{3}\sqrt{2}=\dfrac{36\sqrt{2}-4\sqrt{2}}{3}}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{A_{R}=\dfrac{32\sqrt{2}}{3}}~u.a}}}}$