Question

Calcular a área determinada pelas curvas de equações y = x² – 3x – 4 ; y = 0 ; x = 0 e x = 5.?

Answer 1

$\mathrm{y=x^2-3x-4\ \ \|\ \ x\in{[0,5]}}\\\\\\ \mathrm{\int\limits_0^5x^2-3x-4\ dx=}\\\\ \mathrm{=\bigg(\int x^2\ dx-3\int x\ dx-\int4\ dx\bigg)\bigg|_0^5=}\\\\ \mathrm{=\bigg(\dfrac{x^3}{3}-\dfrac{3x^2}{2}-4x\bigg)\bigg|_0^5=\bigg(\dfrac{2x^3-9x^2-24x}{6}\bigg)\bigg|_0^5=}\\\\ \mathrm{=\bigg(\dfrac{2.5^3-9.5^2-24.5}{6}\bigg)-\bigg(\dfrac{2.0^3-9.0^2-24.0}{6}\bigg)=}\\\\ \mathrm{=\dfrac{2.125-9.25-24.5}{6}=\dfrac{250-225-120}{6}=\dfrac{-95}{6}}$

$\mathrm{S=\bigg|\dfrac{-95}{6}\bigg|\ \to\ \boxed{\mathbf{S=\dfrac{95}{6}\ u.a.}}}$