In this problem, we explore a different method to estimate the area under curvef(x) =xfrom 0 to 4.

Let [x] be the greatest integer that is less than or equal toxR. This is known as thefloor function.

(a) Sketch the functiong0(x) = [x] in the interval [0,4]. Compute the area under the curve ofg0over [0,4]. Is this area an over-estimate or under-estimate for the area underfover [0,4]?

( b)Sketch the functiong1(x) =21[2x] in the interval [0,4]. Compute the area under the curve ofg1. Again, to which estimation method does this area correspond? Is this an over- or under-estimate?