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Sagot :
A new form of the triple integral [tex]\int\limits^1_0 \int\limits^x_0 \int\limits^y_0 f(x,y,z)dzdydx[/tex] as a = 0 b = 1 g2(z) = 1 h2(y,z) = 1.
In other words, we want the integration order to be totally reversed for
[tex]\int\limits^1_0\int\limits^x_0 \int\limits^y_0 f (x,y,z) dz dy dx[/tex]
Keep in mind that this area is quite simple to define. The planes z = y and y = x, as well as the coordinate planes [tex]x=y=z=0[/tex], define our boundaries. We essentially have upper bounds z = y = x = 1 because x ∈[ 0, 1 ]. Therefore, we can alternatively express the region as:-
[tex]0\leq x\leq y\\0\leq y\leq z\\[/tex]
z∈ I0,1I. So
[tex]\int\limits^1_0 \int\limits^x_0 \int\limits^y_0 f(x,y,z)dzdydx = \int\limits^1_0 \int\limits^z_0 \int\limits^y_0 f(x,y,z)dxdydz[/tex]
Remember that a double integral could be set up in two different ways. Our number of alternative orders of integration increases from two to six when we include that third integral. We will rewrite the supplied integral in one of the other five possible orders in this exercise.
To learn more about triple integral, refer:-
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