Question

Approximate the area under the curve on the given interval using n rectangles and the evaluation rules (a)left endpoint, (b) midpoint and (c) right endpoint.

y=(x+2)^(1/2) on [1,4], n=16

How am I suppose to do this?

Answer 1

It looks like they want you to use the trapezoidal rule, which is explained here:
http://metric.ma.ic.ac.uk/integration/techniques/definite/numerical-methods/trapezoidal-rule/

Answer 2

Looks more primitive than trapezoids to me, rectangles.
In each interval, use the y value on the left of that block for the height in part a
In each interval use the y value on the right of that block for part c (you have already calculated most of them for part a because except for the first one on the left, the left in part a becomes the right in part c
Now part b is a pain because you have to calculate new values of y in the middle of each interval and for the area of that block use that height times the interval in x