Evaluate the iterated integral: a)int_0^3 int_0^(pi/3) int_0^4 r xx cos theta drd theta dz b)int_0^(pi/2) int_0^3 int_0^(4 - z) zdrdzd theta

rocedwrp 2021-09-02 Answered

Evaluate the iterated integral:
a) 030π304r×cosθdrdθdz

b) 0π20304zzdrdzdθ

c) 0π20π202ρ2dρdθdϕ

d) 0π40π40cos(ϕ)cosθdρdϕdθ

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Expert Answer

2abehn
Answered 2021-09-03 Author has 88 answers

a) 030π304r×cosθdrdθdz=

=030π3cosθ[γ22]04dθdz=

=030π38cosθ×dθ×dz=

=038×[sinθ]0π3dz=

=038×32dz=

=4303dz=

=43[z]03=

=123

b) 0π20304zzdrdzdθ=

=0π203z×[γ]04zdz×dθ=

=0π203z×[(42)0]dzdθ=

=0π2034zz2×dzdθ=

=0π2[(4z22)z33]03dθ=

=0π2(189)×dθ=

=90π2dθ=

=9[θ]0π2=

=9π2

c)

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