1 5.5Find the triple integral x dV by converting to cylindrical coordinates.Assume that is the solid enclosed by the planes z = 0 and z= x and the cylinder x² + y² = 81.(Give an exact answer. Use symbolic notation and fractions where needed.)MIncorrectD₁xIncorrectxdV=IncorrectxdV=0.xdV=6361265614FeedbackConvert rectangular coordinates to cylindrical coordinates usingx = r cos (0)y = rsin (0)z=zUse partial integration to find the iterated integralr2(0) 22(r.0)To Tori(0)Note that the required solid can be broken into two solids.z1(r,0)f(r, 0, z) r dz dr d0

The given problem is to evaluate the given triple integral of x over the given region E enclosed by…

Answered: 5.5 Find the triple integral x dV by…

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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Let E be the solid region in the first octant bounded by the coordinate planes, the cylinder x2+y2=5y and the sphere x2+y2+z2=25. Write an interated intergral used to solve ∫∫∫Ey dV using: A. Cartesian coordinates B. Cylindrical coordinates without evaluating.
1. a) Find the volume of the solid enclosed between the paraboloids z = 5x^2 + 5y^2and z = 6 − 7x^2 − y^2 using tripple integral. b) Please look at the picture and solve number 2 and 3 for me. Thank you.
Let S be the portion of the cylinder z = 1 − x2, in the first octant and between the planes y = 0 and y = ax, where a is a positive real constant. The value of a for which Area (S) = 53/2−1 is:
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)
5. Find the volume of the solid below the z=x^2+y^2 paraboloid, above the xy-plane, and inside the cylinder x^2+y^2=2x.
8.2) 7) 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.
Determine whether the following statements are true and give an explanation or counterexample. a. When using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. b. If a region is revolved about the y-axis, then the shell method must be used. c. If a region is revolved about the x-axis, then in principle, it is possible to use the disk>washer method and integrate with respect to x or to use the shell method and integrate with respect to y.
6. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, y = 3x; about the y-axis V = ?

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