Question

como fica a integral (×^4-4x^2+6)dx no intervalo de -2 e 2

Answer 1

$\int_{-2}^{2} (x^4-4x^2+6) dx = \left[\frac{x^{4+1}}{4+1} - \frac{4x^{2+1}}{2+1}+6x \right]^{2}_{-2} =\left[\frac{x^{5}}{5} - \frac{4x^{3}}{3}+6x \right]^{2}_{-2} \\\\ = \left( \frac{(2)^5}{5}- \frac{4*(2)^3}{3}+6*(2) \right) - \left( \frac{(-2)^5}{5}- \frac{4*(-2)^3}{3}+6*(-2) \right)\\\\ = \left( \frac{116}{15} \right) - \left( -\frac{116}{15} \right) = \frac{232}{15}$