. Applied calculus; principles and applications . (2) (3) I pdddp = i / p^ddl 0 t/0 Jo J -j27r = ia^d\ = Tra n27r ra 127r pdpde= I pdpdlJo Jo 310 INTEGRAL CALCULUS In (2) the sectors are summed, while in (3) the rings aresummed. In this case of the circle it is to be noted that no limit need be invoked,since the integral is thesum in each case, the in-crements being the differ-entials, the variables allincreasing uniformly. Example 2. — Find thearea between the two tan-*gent circles p = 2a cos6and p = 2 6 cos ^, wherea> —X / 0 t/26co I 0 pdddp = 4:{a^- = 7r(a2-62). Example 3. — Find the
. Applied calculus; principles and applications . (2) (3) I pdddp = i / p^ddl 0 t/0 Jo J -j27r = ia^d\ = Tra n27r ra 127r pdpde= I pdpdlJo Jo 310 INTEGRAL CALCULUS In (2) the sectors are summed, while in (3) the rings aresummed. In this case of the circle it is to be noted that no limit need be invoked,since the integral is thesum in each case, the in-crements being the differ-entials, the variables allincreasing uniformly. Example 2. — Find thearea between the two tan-*gent circles p = 2a cos6and p = 2 6 cos ^, wherea> —X / 0 t/26co I 0 pdddp = 4:{a^- = 7r(a2-62). Example 3. — Find the areas between the cardioid p =2 a (1 — cos 6) and the circle p = 2 a.
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