Consider the function
In this problem you will calculate by using the definition
The summation inside the brackets is which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub-interval.
Calculate for
on the interval [0, 2]
i have no clue on how to do this one.
Right end point: .....[1]
Subdivide the interval [0,2] into n equal parts, then each will have length:
From [1]:
The kth rectangle has area:
=
=
Sum up the rectangles:
Remember, the sum of
Sub into our summation:
=
Now take the limit:
See the limit and, consequently, your integral?.
EDIT: Ol' Topsquark beat me, but after all that I ain't deleting it