Download PROBLEM 4 Use the limit definition of definite integral to evaluate

PROBLEM 4
Use the limit definition of definite integral to evaluate
.
SOLUTION
Divide the interval
for
into
equal parts each of length
. Choose the sampling points to be the right-hand endpoints
of the subintervals and given by
for
. The function is
.
Then the definite integral is
(Use summation rule 6 from the beginning of this section.)
(Use summation rules 5 and 1 from the beginning of this section.)
(Use summation rule 2 from the beginning of this section.)
.