Find the volume of the given solid. Enclosed by the paraboloid z = 5x^2 + 2y^2 and the planes x...

Question:

Find the volume of the given solid. Enclosed by the paraboloid {eq}z = 5x^2 + 2y^2 {/eq} and the planes x = 0, y = 4, y = x, z = 0.

Volume enclosed:

You have to find the volume of the given paraboloid {eq}z = 5x^2 + 2y^2 {/eq} and you have given all of the needed bounds which help you to perform your task.

Answer and Explanation:

The given region is actually below the paraboloid. So, you have given {eq}0 \le z \le 5{x^2} + 2{y^2},0 \le x \le 4,x \le y \le 4 {/eq}.

The volume...

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How to Find Volumes of Revolution With Integration

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