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Webwork Question 1

cbrowni1

I am not exactly sure what I am supposed to find, I think the notation is a bit confusing for me. Could anyone help me out?

mark

First off, the notation

L_f(P) \text{ and } U_f(p)

stands for lower and upper sums, which is a bit different from what we’ve used in class. If you graph the function f(x) = x\sin(x) ove the interval [0,\pi/2], though, you’ll notice that it’s strictly increasing on that interval. Thus,

A right hand sum should be an upper bound and
a left hand sum should be a lower bound.

I guess the right sum using the partition they present should look something like so:

Now, you just add up the areas of those rectangles. The last rectangle, for example, has area

L\times H = \frac{\pi}{6} \times \frac{\pi}{2}.

Note that there’s not just one \Delta x; the outer two rectangles are wider than the inner two.