Given
we are given a function
over the interval [0,5].
Required
we need to find formula for Riemann sum and calculate area under the curve over [0,5].
Explanation
If we divide interval [a,b] into n equal intervals, then each subinterval has width
and the endpoints are given by
For k=0 and k=n, we get
Each rectangle has width and height as
we sum the areas of all rectangles then take the limit n tends to infinity to get area under the curve:
Here
Now Area=
So the required area is 66.6 sq units.