10 square units.
.........................
Split up the interval [2, 5] into
equally spaced subintervals, then consider the value of
at the right endpoint of each subinterval.
The length of the interval is
, so the length of each subinterval would be
. This means the first rectangle's height would be taken to be
when
, so that the height is
, and its base would have length
. So the area under
over the first subinterval is
.
Continuing in this fashion, the area under
over the
th subinterval is approximated by
, and so the Riemann approximation to the definite integral is
and its value is given exactly by taking
. So the answer is D (and the value of the integral is exactly 39).
So here are the rules of horizontal asymptotes:
- Degree of Numerator > Degree of Denominator: No horizontal asymptote
- Degree of Numerator = Degree of Denominator:
- Degree of Numerator < Degree of Denominator: y = 0
Looking at the rational function, since the degree of the numerator is 2 and the degree of the denominator is 1 (and 2 > 1), this means that <u>this function has no horizontal asymptote.</u>