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Use a parametrization to find the flux {eq}\iint_SFnd\sigma {/eq} of the field F = 5z k across the portion of the sphere {eq}x^2 y^2 z^2 = 100 {/eq} in the first octant in the direction away

Dx = " 3x2 2 − x3 2 # 1 x=0 = 1 Note that Methods 1 and 2 give the same answer If they don't it means something is wrong 011 Example Evaluate ZZ D (4x2)dA where D is the region enclosed by the curves yIn other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16 Explanation Using synthetic division and the fact that x = − 1 is obviously a solution we find that we can expand this to (x 1)(x2 −x 1) = 0 In order to have LHS=RHS need one of the brackets to be equal to zero, ie (x 1) = 0 1 (x2 − x 1) = 0 2 From 1 we note that x = −1 Quadratic Function Y x3 1 y 0 x 0 x 2