Find the volume of the solid lying under elliptic paraboloid

Reference no: EM131012478

1. Find the volume of the solid lying under the elliptic paraboloid x²/4 + y²/9 + Z = 1 and above the rectangle R = [-1, 1] times [-2, 2].

2. a. Sketch the region of the integration and change the order of integration of ₀∫¹ _3y∫³ e^{x^2} dx dy.

b. Evaluate the integral ₀∫¹ _3y∫³ e^{x^2} dx dy by evaluating the integral in (a) in which the order of integration has been reversed

3. Evaluate the integral ∫_D √16 - x² -y² dA by changing to polar cooridination, where D is the region that lies between the circles x² + y² = 16. [Note the integral represents the volume of the solid that is inside the sphere x² + y² + z² = 16 and outside the cylinder x² + y² = 4]

Reference no: EM131012478

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