The value of the double integral for the function f(x, y) and the given region R is -60.
We can use the double integral to translate our understanding of volumes under surfaces in a three-dimensional coordinate system from areas under curves in a two-dimensional coordinate system. Just two of the many uses for double integrals are the ability to compute mass densities and estimate probability density functions.
We may get the volume under the area enclosed by the region using the double integral. By evaluating integrals with respect to only one variable while holding the other variable constant, we can compute double integrals.
Given function is: f(x, y) = 8xy³; R is the rectangle defined by -2 ≤ x ≤ 0 and -1 ≤ y ≤ 2.
Firstly integrate w.r.t y and apply the limits, similarly integrate w.r.t x and apply the corresponding limits.
The value of this double integral is calculated to be -60.
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