Question

f:R ->R; f(x) = 3x - x². Calculeaza $\int\limits^3_0 {f ^{2} } \, (x) dx$

Answer 1

Notez integrala de calculat cu I. Avem
$I=\int_0^3(9x^2-6x^3+x^4)dx=\left(\dfrac{9x^3}{3}-\dfrac{6x^4}{4}+\dfrac{x^5}{5}\right)|_0^3=$

$=x^3\left(3-\dfrac{3x}{2}+\dfrac{x^2}{5}\right)\Displaystyle|_0^3=27\left(3-\dfrac92+\dfrac95\right)=32,4.$