ーx2 +ッSSS.Convert the in tegralisCYlindricar coordinetes a.youtae integral af ter you2x42 dz dxintointegral inanCYlindeicaldo ñothaveto evalvakCONvertiti

Answered: Convert the integral 2x42 dz dx into 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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ーx2 +ッ
SSS.
Convert the in tegral
is
CYlindricar coordinetes a.you
tae integral af ter you
2x42 dz dx
into
integral in
an
CYlindeical
do ñot
have
to evalvak
CONvertiti

Expert Solution

Step 1

$w e c o n v e r t t h e r e c \tan g u l a r c o - o r d i n a t e s i n t o c y l i n d r i c a l c o - o r d i n a t e s \int \int \int f (x, y, z) d x d y d z = \int \int \int f (r \cos θ, r \sin θ) r d z d r d θ p u t x = r \cos θ, y = r \sin θ a n d z = z g i v e n \int_{0}^{3} \int_{0}^{\sqrt{9 - x^{2}}} \int_{0}^{\sqrt{x^{2} + y^{2}}} 2 x y z d z d y d x = \int_{0}^{π} \int_{0}^{3} \int_{0}^{r} 2 r \cos θ r \sin θ z r d z d r d θ = \int_{0}^{π} \int_{0}^{3} \int_{0}^{r} r^{3} \sin 2 θ z d z d r d θ$

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