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 />
Examples, XIII<br />
Example (cont<strong>in</strong>ued)<br />
Therefore:<br />
V = 2π<br />
� � 1<br />
2<br />
�<br />
1<br />
r<br />
0 4 − r 2 dr +<br />
� �<br />
1 1<br />
= 2π +<br />
24 48<br />
= π<br />
8 .<br />
� 1<br />
2<br />
0<br />
r<br />
2 − r 2 �<br />
dr