Question

Calcular a Área usando a integral:
$\int\limits^2_0 {(1+x^{2}-4-2x) } \, dx$

Answer 1

$A(R) = - \displaystyle\mathsf{\int\limits_{0}^{2}(1+x^{2}-4-2x)dx}\\A(R) = - \displaystyle\mathsf{\left[x+\dfrac{1}{3}.x^{3}-4x-x^{2}\right] </p><p>_{0}^{2}}$

$\mathsf{A_{(R)} = -[2+\dfrac{1}{3}.2^{3}-4.2-2^{2}}] \\\mathsf{A_{(R)}=-[2+ \dfrac{8}{3}-8-4}]\\\mathsf{A_{(R)} =[\dfrac{6+8-24-12}{3}}]$

$\mathsf{A_{(R)}=\dfrac{22}{3}}$