Question

Calcular as áreas da região limitada

Pela curva y = -x2 + 9 e o eixo x no intervalo em x de [-1/2, 1]

Answer 1

$Area = \int\limits^{1}_{- \frac{1}{2} } {-x^2+9} \, dx \\\\\\Area= \left \frac{-x^3}{3}+9x \right]^1_{- \frac{1}{2}}\\\\Area= ( \frac{-1^3}{3}+9*1) - ( \frac{-( \frac{-1}{2})^3}{3}+9*( \frac{-1}{2})) \\\\Area= \frac{105}{8}$