Ensino Superior ⇒ Integral tripla

[menelaus]

Exprima a integral [tex3]\int\limits_{0}^{\pi}\int\limits_{\frac{3\pi}{4}}^{\pi}\int\limits_{0}^{1}p^5. cos\theta . sen^2\alpha \ dp \ d\alpha \ d\theta [/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\int\limits_{0}^{\pi}\int\limits_{\frac{3\pi}{4}}^{\pi}\int\limits_{0}^{1}p^5. cos\theta . sen^2\alpha \ dp \ d\alpha \ d\theta [/tex3]

como integral iterada em coordenadas retangulares.

Resposta

---

[tex3]\int\limits_{-\frac{\sqrt{2}}{3}}^{\frac{\sqrt{2}}{2}}\int\limits_{0}^{\sqrt{\frac{1}{2}-x^2}}\int\limits_{-\sqrt{1-x^2-y^2}}^{-\sqrt{x^2+y^2}}x.(x^2+y^2+z^2) \ dz \ dy \ dx[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\int\limits_{-\frac{\sqrt{2}}{3}}^{\frac{\sqrt{2}}{2}}\int\limits_{0}^{\sqrt{\frac{1}{2}-x^2}}\int\limits_{-\sqrt{1-x^2-y^2}}^{-\sqrt{x^2+y^2}}x.(x^2+y^2+z^2) \ dz \ dy \ dx[/tex3]

.