Question

Calcular as áreas da região limitada
a) pela curva y= x2 - 2x + 10 e y = 0 no intervalo em x de [-2,4].

Answer 1

$Area= \int\limits^{4}_{-2} {(x^2-2x+10)} \, dx \\\\Area= \left[ \frac{x^{2+1}}{2+1}-2 \frac{x^{1+1}}{1+1}+10x \right]^4_{-2}\\\\Area= \left[ \frac{x^{3}}{3}-x^2+10x \right]^4_{-2}\\\\\\Area= \left(\frac{4^{3}}{3}-4^2+10*4 \right) - \left(\frac{(-2)^{3}}{3}-(-2)^2+10*(-2) \right)\\\\Area = \frac{136}{3}-\left( \frac{-80}{3}\right) =72$