24. Center of mass A solid of constant density is bounded be- low by the plane z = 0, on the sides by the elliptical cylinder x² + 4y2 = 4, and above by the plane z = 2 – x (see the ac- companying figure). a. Find x and ỹ. b. Evaluate the integral •(1/2)V4-x² r2-x Mx z dz dy dx -(1/2)V4-x²Jo using integral tables to carry out the final integration with respect to x. Then divide My by M to verify that 7 = 5/4. z = 2 - x -2 x² + 4y? = 4 %3D 2.

24. Center of mass A solid of constant density is bounded be- low by the plane z = 0, on the sides by the elliptical cylinder x² + 4y2 = 4, and above by the plane z = 2 – x (see the ac- companying figure). a. Find x and ỹ. b. Evaluate the integral •(1/2)V4-x² r2-x Mx z dz dy dx -(1/2)V4-x²Jo using integral tables to carry out the final integration with respect to x. Then divide My by M to verify that 7 = 5/4. z = 2 - x -2 x² + 4y? = 4 %3D 2.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.3: Volume And Average Value

Problem 19E

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