Question

Calcule a integral dupla: ∫ 4 variando 2 ∫ 2variando 1 ( x ² + y ² ) dydx

Answer 1

divida em duas integrais:

$\int\limits^1_2 { x^{2} + y^{2}} \, dy = x^{2} + \frac{7}{3} \\\\\int\limits^2_4 {x^{2} + \frac{7}{3}} \, dx  = \frac{70}{3}$

Answer 2

∫ 4 variando 2 ∫ 2variando 1 ( x ² + y ² ) dydx

∫ 4 variando 2 [ 2variando 1 ( yx ² + y³/3 ) ] dx

∫ 4 variando 2  ( 2x²+8/3 -x²-1/3)  dx

∫ 4 variando 2  ( x²+7/3)  dx

4 variando 2  ( x³/3+7x/3)  

=4³/3 +28/3 -8/3-14/3

=64/3 +28/3-8/3-14/3 =70/3