Calka
Marny student : ∫(od −∞ do +∞) x2*e−x2/2dx
8 sty 20:53
jc:
| | −1 | | −x | | 1 | |
całka nieoznaczona = |
| ∫x (e−x2)' dx = |
| x e−x2 + |
| ∫e−x2 dx |
| | 2 | | 2 | | 2 | |
| | 1 | |
∫−∞∞ x2 e−x2 dx = |
| ∫−∞∞ e−x2 dx |
| | 2 | |
8 sty 21:02
Adamm:
= 2∫0∞ x2e−x2/2 dx
u = −x2/2
du = −x dx
2 ∫0−∞ −(−2u)1/2eu dx = 2√2 Γ(3/2) = √2 Γ(1/2) = √2π
8 sty 21:09