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Solving for a "Double Integral"

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Question: Evaluate the double integral xy dA where R is the region bounded by the graphs of y= square root x, y= 1/2x, x=2, x=4

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Solution Summary

This solution provides a detailed, step-wise response which depicts carefully how to evaluate the given double integral. Two attachments are also included in this solution, both .png files, in which one contains a sketch of the graph for this double integral and the other contains the integral.

Solution Preview

The first step is to sketch the graph, plotting the four different curves given, and to identify the region bounded by these curves.
(Please refer to the attachment - "Graph.png")

The equation
y = (square root of x)
represents a parabola which opens to the right.
[This is easy to note, since y = (sqrt)x means y^2 = x, that is, x = y^2: which means if the value of x is calculated, given values of y, we will get the same value for y and -y, since (-y)^2 = y^2. That is, x = y^2 will be symmetric about the x-axis, and obviously will take positive values, meaning the curve lie ...

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