Calculer \(I_1 = \iint\limits_{D} (x + y)e^{-x}e^{-y}dxdy\) où \(D = \left\{ (x, y)\in \Rr^{2}/x, y\geq 0, x + y \leq 1\right\}\).
Calculer \(I_2 = \iint\limits_{D} (x^{2} + y^{2})dxdy\) où \(D = \left\{ (x, y)\in \Rr^{2}/x^{2} + y^{2}<x, x^{2} + y^{2}>y\right\}\).
Calculer \(I_3 = \iint\limits_{D} \frac{xy}{1 + x^{2} + y^{2}}dxdy\) où \(D = \left\{ (x, y)\in [0, 1]^{2}/x^{2} + y^{2} \geq 1\right\}\).
Calculer \(I_4 = \iint\limits_{D} \frac{1}{y\cos (x) + 1}dxdy\) où \(D = [0, \frac{\pi}{2}]\times [0, \frac{1}{2}]\).
Calculer \(I_5 = \iiint\limits_{D} zdxdydz\) où \(D = \left\{ (x, y, z)\in (\Rr^{ + })^{3}/y^{2} + z \leq 1, x^{2} + z \leq 1\right\}\).
Calculer \(I_5 = \iint\limits_{D} xydxdy\) où \(D = \left\{ (x, y)\in \Rr^{2}/x, y>0, \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \leq 1\right\}\) avec \(a, b>0\).