Question

FUNCIÓN INTEGRAL EJERCICIO:
Ayuda por favor

Answer 1

Respuesta:

Explicación paso a paso:

$\int_{1}^{2}{(-x^{2}+4x+3)}\,dx\\\\\int_{1}^{2}{(-x^{2}+4x+3)}\,dx=\int_{1}^{2}{-x^{2}}\,dx+4\int_{1}^{2}{x}\,dx+3\int_{1}^{2}{dx}=\\\\=\left(-\frac{x^{3}}{3}\right)_{1}^{2}+2\left(x^{2}\right)_{1}^{2}+3\left(x\right)_{1}^{2}=-\frac{2^{3}}{3}-\left[-\frac{1}{3}\right]+2\left(2^{2}-(1^{2})\right)+3(2-1)=\\\\=-\frac{8}{3}+6+3=\frac{19}{3}$