Please complete problem 19 and show work :) 19-20 Set up the triple integral of an arbitrary continuous function f (x, y, z) in cylindrical orspherical coordinates over the solid shown.19.yAnswer +20.21-22(a) Express the triple integral // f (x, y, z, ) dV as an iterated integral in spherical coordinatesfor the given function ƒ and solid region E.(b) Evaluate the iterated integral.21. f(x, y, z) = Væ² + y? + z²- y² + z² = 4x²+ y? +z? = 9

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Answered: 19-20 Set up the triple integral of an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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How do I set up the triple integral of the function xy2 -3z, where the solid is bounded by the sphere x2 + y2 + z2 = 25, the cylinder x2 + y2 = 9, and the xy-plane, using spherical coordinates? Solving these integrals by hand is way too difficult, so I just need to find the limits of integration in terms of ρ, φ, and θ.
1)Sketch the solid obtained by rotating the region bound byy=2√x and y=x, about the line x =−2. 2)Write the expression for the area of a representative washer 3)Set up and solve the definite integral used to calculate the volume of the solid in (1)
28- Which of the following double integral allows to calculate the moment of inertia about the y-axis of the plate object with surface density f(x, y) = xy^3, bounded by the graphs of the functions y=x^2 and y=x+2?
Let G be a solid shape enclosed by a surface x*2+ y*2 = 1, z = 0 and z = x*2+ y*2+ 1. 1) Draw the solid shape G given for 2) Convert Triple integrals(x*2+ y*2+ z*2) dV into a triple integral in the cylindrical coordinate system G. and specify the upper and lower bounds of the integration of all variables without Calculate the answer in numbers
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8.2) 5) The given curve is rotated about the yaxis. Set up, but do not evaluate, an integral for the area of the resulting surface by inte grating (a) with respect to x and (b) with respect to y.
first set up a double integral using rectangular coordinates. for a solid bounded below xy-plane and above the plane 4=x+z+2y and is between x^2+6y^2=1 and x^2+6y^2=8. then write the region in cylidrical and spherical coordinates
11. Evaluate the double integral , (1-x)dA where R = [0, 1] x [0.2] by first identifying it as the volume %3D | of the solid. Sketch the solid.
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Let E denote the region in the 1st octant bounded between the planes x = 0, z = 0, y = 4, 2y −z = 0 and the surface z = 8−2x2 (see diagram to the right). Set up but DO NOT EVALUATE iterated integrals equivalent to ∫E f(x, y, z) dV in each of the following orders. Show enough supporting work so that your reasoning is clear, and circle your final answers. (a) The “dx dz dy” order.(b) The “dy dz dx” order.
Since the R integration region is the region bounded by the hyperbolas x2 - y2 = 1, x2 - y2 = 9, xy = 4 and xy = 2 in the first region, with the help of u = xy and v = x2 - y2 transformation ∫∫R ( x2 + y2) dA What is the value of the integral?a) 0b) -7c) 7d) 8e) none

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19-20 Set up the triple integral of an arbitrary continuous function f (æ, y, z) in cylindrical or spherical coordinates over the solid shown. 19. y