Triple integrals in cylindrical and spherical coordinates
Triple integrals in cylindrical and spherical coordinates
Triple integrals in cylindrical and spherical coordinates
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MATH 209—<br />
Calculus,<br />
III<br />
Volker Runde<br />
<strong>Triple</strong><br />
<strong><strong>in</strong>tegrals</strong> <strong>in</strong><br />
cyl<strong>in</strong>drical<br />
coord<strong>in</strong>ates<br />
<strong>Triple</strong><br />
<strong><strong>in</strong>tegrals</strong> <strong>in</strong><br />
<strong>spherical</strong><br />
coord<strong>in</strong>ates<br />
Integration <strong>in</strong> <strong>spherical</strong> coord<strong>in</strong>ates, I<br />
Def<strong>in</strong>ition<br />
A set of the form<br />
{(r, θ, φ) : r ∈ [a, b], θ ∈ [α, β], φ ∈ [c, d]}<br />
with a ≥ 0, β − α ≤ 2π, <strong>and</strong> d − c ≤ π is called a <strong>spherical</strong><br />
wedge.<br />
Question<br />
How does one evaluate ���<br />
wedge?<br />
E<br />
f (x, y, z) dV if E is a <strong>spherical</strong>