Respuesta :
By using the triple integral, the wedge's volume is 4/15.
What is parabolic cylinder?
A parabolic cylinder is a three-dimensional quadratic surface (sometimes known as a quadric surface) in mathematics, specifically analytical geometry, and is defined by the equation x 2 + 2 a y = 0 x2+2ay=0. A parabola serves as the directrix of a parabolic cylinder, to put it another way.
According to the assertion:
The wedge's volume, which the parabolic cylinder encloses, must be determined.
Consequently, as a result of the z=y form,
In addition to the specified boundary, the plane y=0 x = 0, z = 0.
For all of this, we are therefore in the first octant. additionally, the plane
x + y = 1 is a constraint.
Triple integrals are three independent integrations that are done one after the other to calculate a volume or to integrate across three independent dimensions in a fourth dimension.
The following would be written as a triple integral:
∫x=0 ∫y=0
∫z=0 dy dz dx
Once the values have been entered and the problem has been solved, we obtain the
[−4/15(1−x)^5/2] at x=0
The answer will then change to 4/15.
As a result, using the triple integral, the wedge's volume comes out to 4/15.
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