Sketch the region enclosed by the given curves.

y = 4/X
y = 16x, y = 1X/16
x > 0
and the area between the curves

change the 16log(2) to 16ln(2) and then the answer is correct.

excellent! thanks a lot!

Can you sketch the curves?

yes i just need the area i didn't know how to sketch it on here

thank you!

or that's not right

If I read it correctly, you have

y=4/x, y=16x, and y=x/16 for x>0

You need to break the area into two regions, because the two top curves intersect at x = 1/2

So the area is

∫[0,1/2] 16x - x/16 dx + ∫[1/2,8] 4/x - x/16 dx
= (8x^2-x^2/32)[0,1/2] + (4logx-x^2/32)[1/2,8]
= 255/128 + (4log16 - 255/128)
= 4log16 = 16log2