(a) Given that, the function is on the interval
It is known that, the formula for the Riemann-sum is where
Obtain the value of
Divide the interval into sub-intervals with length as and the right end-points are . Find the area under the curve over by using the right-end points as follows,
Therefore, the area under the given curve over by the right-end points approximation is 141.75.
(b) The left end-points are
Find the area under the curve over by using the left-end points as follows,
Therefore, the area under the given curve over by the left-end points approximation is 213.75.