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Find the volume of the region bounded a above by the elliptical paraboloid z = 10 + x² + 3y² and below by the rectangle R: 0 ≤ x ≤ 1,0 ≤ y ≤2? Find the volume of the region bounded a above by the paraboloid z = x² + y² and below by the square R: -1 ≤ x ≤ 1,-1 ≤ y ≤ 1? Evaluate the following integral: 1) f*f*2xy dy dx 1 y 1 + xy 26. S. 3) (² + √y) dx dy SS =[[*xy e²dy dx 2 dx dy TL 2 0 C.S. | | (sinx + 2π T TL y sin x dx dy Exercises (sin x + cos y)dy dx Abbas ALAlusi

Find the volume of the region bounded a above by the elliptical paraboloid z = 10 + x² + 3y² and below by the rectangle R: 0 ≤ x ≤ 1,0 ≤ y ≤2? Find the volume of the region bounded a above by the paraboloid z = x² + y² and below by the square R: -1 ≤ x ≤ 1,-1 ≤ y ≤ 1? Evaluate the following integral: 1) f*f*2xy dy dx 1 y 1 + xy 26. S. 3) (² + √y) dx dy SS =[[*xy e²dy dx 2 dx dy TL 2 0 C.S. | | (sinx + 2π T TL y sin x dx dy Exercises (sin x + cos y)dy dx Abbas ALAlusi

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
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Exercises Find the volume of the region bounded a above by the elliptical paraboloid z = 10 + x² + 3y² and below by the rectangle R: 0 ≤ x ≤ 1,0 ≤ y ≤2? Find the volume of the region bounded a above by the paraboloid z = x² + y² and below by the square R: -1 ≤ x ≤ 1,-1 ≤ y ≤ 1? Evaluate the following integral: 1) ff*2xy dy dx 1 -1 y ₁ dx dy 1 + xy 2) [²√ ² 3) [* S* (7 + √5) dx dy SS²³ 4) 5) [f² 7) 8) 9) -2π TL SS R 10) xy exdy dx y sin x dx dy J(1) R So R xy cos y dA Co ff xy ey* dA e² (sin x + cos y)dy dx Abbas ALAlusi dA R: 0≤x≤ 4, 1≤ y ≤2 R: -1 ≤ x ≤ 1,0 ≤ y ≤n R: 0≤x≤2, 0≤ y ≤1 fa-x²-y (1 − x² - y²)dA R is the unit circle on the xy - plane?
Transcribed Image Text:Exercises Find the volume of the region bounded a above by the elliptical paraboloid z = 10 + x² + 3y² and below by the rectangle R: 0 ≤ x ≤ 1,0 ≤ y ≤2? Find the volume of the region bounded a above by the paraboloid z = x² + y² and below by the square R: -1 ≤ x ≤ 1,-1 ≤ y ≤ 1? Evaluate the following integral: 1) ff*2xy dy dx 1 -1 y ₁ dx dy 1 + xy 2) [²√ ² 3) [* S* (7 + √5) dx dy SS²³ 4) 5) [f² 7) 8) 9) -2π TL SS R 10) xy exdy dx y sin x dx dy J(1) R So R xy cos y dA Co ff xy ey* dA e² (sin x + cos y)dy dx Abbas ALAlusi dA R: 0≤x≤ 4, 1≤ y ≤2 R: -1 ≤ x ≤ 1,0 ≤ y ≤n R: 0≤x≤2, 0≤ y ≤1 fa-x²-y (1 − x² - y²)dA R is the unit circle on the xy - plane?
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