Question

Fie F primitiva functiei f:R->R, f(x)= x^2+2x care se anuleaza in punctul x=1. Sa se calculeze F(2)

Answer 1

$\int\limits{x^3+2x} \, dx = \frac{x^3}{3} +x^2+C \\ F(1)=0 \\ \frac{1^3}{3} +1^2+C=0 \\ C=- \frac{4}{3} \\ F(x)= \frac{x^3}{3}+x^2- \frac{4}{3} \\ F(2)= \frac{8}{3} +4- \frac{4}{3}= \frac{16}{3}$