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In this video we are going to find the volume of the given solid under the paraboloid z equals x squared plus 4y squared.
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And it's above the rectangle r, which is the closed interval from 0 to 2 cross the closed interval from 1 to 4.
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And this is a double integral setup.
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And here's how this is going to work.
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So to get the volume, this is going to be a double integral of x squared plus 4y squared.
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We'll go dy dx.
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Now my y limits go from 1 to 4 and my x limits go from 0 to 2.
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Now to do a double integral, we got to evaluate the innermost integral first.
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So in other words, we're going to do a partial integral from 1 to 4 of x squared plus 4y squared dy.
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And when you integrate with respect to y, x is constant.
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So you're going to get x squared y plus 4y cubed divided by 3 evaluated from y equals 1 to y equals 4 dx.
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Just like this...