At this stage,we take the limit as approachesinfinity. Noticethat the whenyou substituteinfinityinto the
function,the denominatorof the expression beingan exponentialfunction,will approachin-
finity at a muchfasterrate than will the numerator. Thusthis expressionwill approachzero at infinity. Hence
So the volumeof the solid is
Example6:
Evaluate.
Solution:
This can be a toughintegral!To simplify, rewritethe integrandas
Substituteinto the integral:
Using -substitution,let
Returningto our integralwith infinitelimits,we split it into two regions.Chooseas the split pointthe convenient
Takingeachintegralseparately,