Solved: ?In the following exercises, change the order of integration and evaluate the

Chapter 5, Problem 106

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In the following exercises, change the order of integration and evaluate the integral.

Let g be a positive, increasing, and differentiable function on the interval [a, b]. Show that the volume of the solid under the surface z = g′(x) and above the region bounded by y = 0, y = g(x), x = a, and x = b is given by \(\frac{1}{2}\left(g^{2}(b)-g^{2}(a)\right)\)

Text Transcription:

frac_1/2_left(g^2(b)-g^2(a)right)