Write 506.137 in expanded form
1 answer:
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a. The area of is given by the integral
b. Use the shell method. Revolving about the
-axis generates shells with height
when
, and
when
. With radius
, each shell of thickness
contributes a volume of
, so that as the number of shells gets larger and their thickness gets smaller, the total sum of their volumes converges to the definite integral
c. Use the washer method. Revolving about the
-axis generates washers with outer radius
, and inner radius
if
or
if
. With thickness
, each washer has volume
. As more and thinner washers get involved, the total volume converges to
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d. The side length of each square cross section is when
, and
when
. With thickness
, each cross section contributes a volume of
. More and thinner sections lead to a total volume of
