Question

Use the upper and lower sums of 8 rectangles to find two approximations of the area between f(x)=√x+2 and the x-axis over the interval [0,2]

* the square root is only over the x, not over the whole equation.

Answer 1

@jerrijones are you still here?

Answer 2

this is what we are suppose to be looking at



we can start from the left endpoint which is 0 and draw 8 rectangles all with equal bases until we get to the right endpoint 2


so we want 8 rectangles
to figure out what the length of the bases should be all we have to do is calculate
\[\frac{\text{ right endpoint } - \text{ left endpoint } }{n}\]
where n is the number of rectangles you want
then you will find the area of each of these 8 rectangles and then add them up


this is clearly a lower sum since all the rectangles are under the curve




------------------------------------------------

now you would do the same thing but going from the other way
start at the right endpoint and draw your 8 rectangle
find the area of each and then add them up
you will see this will give you an upper sum