Question

Determine a área da região sombreadas

Answer 1

g(x)-f(x)=-x²-2x-(x²-4)

g(x)-f(x)=-2x²-2x+4

$\int\limits^1_{-2} {-2x^{2}-2x+4 } \, dx$

$[-\frac{2x^3}{3}- \frac{2x^2}{2}+4x]_{-2}^1$

$(-\frac{2}{3}-\frac{2}{2}+4)-(\frac{16}{3}-\frac{8}{2}-8)$

$-\frac{2}{3} -\frac{16}{3} -1+4+4+8$

$-\frac{18}{3}+15$

$-6+15$

$9$