Răspuns:
[tex]\int_{0}^{1}{x\sqrt{1-x^2}dx}=\frac{1}{3} [/tex]
Explicație pas cu pas:
[tex]\int_{0}^{1}{x\sqrt{1-x^2}dx}\\
=\dfrac{-1}{2}\int_{0}^{1}{-2x\sqrt{1-x^2}dx}\\
=-\dfrac{1}{2}\int_{0}^{1}{\sqrt{1-x^2}d\left(1-x^2\right)}\\
=-\dfrac{1}{2}\left[\dfrac{(1-x^2)^{3/2}}{3/2}\right]_{0}^{1}\\
=-\dfrac{1}{2}\left(-\dfrac{2}{3}\right)\\
=\dfrac{1}{3}[/tex]
[tex] \hfill{\boxdot} [/tex]
