Question

passo a passo integral definida:
integral (1 a 3) de(-x²+4x-3) dx

Answer 1

$\int\limits^3_1 {(-x^2+4x-3)} \, dx = \left[ -\frac{x^3}{3}+4\frac{x^2}{2}-3x \right]\limits^3_1\\\\ = \left[ -\frac{(3)^3}{3} + 2(3)^2 - 3(3)\right] - \left[- \frac{(1)^3}{3}+2(1)^2-3(1) \right] \\\\ = (-9+18-9) - ( \frac{-1}{3}+2-3 )\\\\ =0-(- \frac{4}{3}) = \frac{4}{3}$