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a) A triple integral I is written using spherical coordinates as follows, p* cos o sin o d0 dodp. i) Sketch the region of integration ii) Rewrite the integral I in cartesian coordinates, using the standard coordi NS nate transformation, I= psin o cos 0, You do not need to evaluate this integral. y = psin o sin 0, z= pcos o.

a) A triple integral I is written using spherical coordinates as follows, p* cos o sin o d0 dodp. i) Sketch the region of integration ii) Rewrite the integral I in cartesian coordinates, using the standard coordi NS nate transformation, I= psin o cos 0, You do not need to evaluate this integral. y = psin o sin 0, z= pcos o.

Advanced Engineering Mathematics
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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Needed to be solve part a completely in 20 minutes and get thumbs up please show neat and clean work please do in 20 minutes
a) A triple integral I is written using spherical coordinates as follows, I = p* cos o sin o d0 do dp. NS i) Sketch the region of integration ii) Rewrite the integral I in cartesian coordinates, using the standard coordi nate transformation, I = psin o cos 0, y = psin o sin 0, You do not need to evaluate this integral. z = pcos o. b) Consider a regular tetrahedron T with vertices 1,0, -1,0, 0, 1, The coordinate transformation G(u, v, u) where (x(u, v, w), y(u, v, u), z(u, v, w)), (-) () ( 1 I(u, v, w) = -2u-v-w+1, y(u, v, w) = v-w, z(u, v, w) = V2v+V2u-
Transcribed Image Text:a) A triple integral I is written using spherical coordinates as follows, I = p* cos o sin o d0 do dp. NS i) Sketch the region of integration ii) Rewrite the integral I in cartesian coordinates, using the standard coordi nate transformation, I = psin o cos 0, y = psin o sin 0, You do not need to evaluate this integral. z = pcos o. b) Consider a regular tetrahedron T with vertices 1,0, -1,0, 0, 1, The coordinate transformation G(u, v, u) where (x(u, v, w), y(u, v, u), z(u, v, w)), (-) () ( 1 I(u, v, w) = -2u-v-w+1, y(u, v, w) = v-w, z(u, v, w) = V2v+V2u-
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