Question

Sketch the region enclosed by the given curves.
y = 4/X
y = 16x, y = 1X/16
x > 0
and the area between the curves

Answer 1

Can you sketch the curves?

Answer 2

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

Answer 3

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

Answer 4

thank you!

Answer 5

or that's not right

Answer 6

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

Answer 7

excellent! thanks a lot!