Calculate the double integral of f(x, y) over the triangle in the figure below.
In order to integrate over this triangular region, we need the equations of the upper and lower bounds.
Find the equation of the lower bound.
y =
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 the equation of the upper bound.
y =
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 these bounds are in terms of x and the integrand is without the variable y, it is easiest to express the triangle as M2jxtJGVDpVt/Kx8Ux1JJ4ofYkdaWFI9ZSKzvQ== simple.
Consider the following figure.
State the inequalities of the vertically simple region defined by the triangle.
0 ≤ x ≤ h4XZagboIgc=
and
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 up the double integral with the triangle as vertically simple.
Integrate.