Due date: Thursday 1/15, 11:59pm
Shells
01
01
Link to originalShells volume - offset graph,
-axis Consider the region in the first quadrant bounded by the lines
, , , and the curve . Revolve this about the -axis. Find the volume of the resulting solid.
Solution
Solutions - 0030-01
(1) Set up integral.
(2) Perform
-substitution with and :
(3) Integrate with power rule:
Link to original
IBP
02
01
Link to originalIntegration by parts - A and E
Compute the integral:
Solution
Solutions - 0010-01
(1) Select
and considering LIATE:
(2) Apply IBP formula
:
Note A: We can change notation
Link to originalto because the value of is arbitrary.
03
02
Link to originalIntegration by parts - A and T
Compute the integral:
Solution
Solutions - 0010-02
(1) Select
and considering LIATE:
(2) Apply IBP formula
:
(3) Select another
and and do IBP again:
(4) Put all together in (A):
Note B: We can change notation
Link to originalto because the value of is arbitrary.