Volume Under the Surface 1 Plus 4xy

Find the volume under the surface $f(x, y) = 1 + 4xy$ where $x$ ranges from 0 to 1 and $y$ ranges from 1 to 3.

Calculating the volume under a surface involves understanding the concept of double integrals, where integration is performed over a specific region in the xy-plane. To solve such problems, one must set up the appropriate bounds for the variables and integrate the given function over the defined range. This requires a solid grasp of integration techniques and the ability to visualize three-dimensional regions.

Additionally, recognizing how the function behaves within the specified domain can aid in efficiently evaluating the integral and interpreting the result in the context of the problem. Mastery of these concepts not only facilitates accurate volume calculations but also enhances overall problem-solving skills in multivariable calculus.

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