Sketch the region in the first quadrant enclosed by y=8/x, y=4x, and y=1/4x. Decide whether to integrate with respect to x or y. Then find the area of the region. Can someone please help me out with showing the work and not giving me some BS speech.

Answer 1

you are taking calculus, and you cannot draw two lines and an hyperbola? There are lots of online graphing sites; maybe you should spend some time working on this, rather than just carping and waiting.

Try this:

http://www.wolframalpha.com/input/?i=plot+y%3Dx%2F4,+y%3D4x,+y%3D8%2Fx

Answer 2

as for the area, it's best to use horizontal strips (why?) of thickness dy. Then the area is

a = ∫[0,√32] 8/y - y/4 dy

Answer 3

Oops. That's not quite right. Can you spot my error?

Also, it is no better to take horizontal rather than vertical strips. For vertical strips

a = ∫[0,√2] 4x - x/4 dx
+ ∫[√2,√32] 8/x - x/4 dx