Sketch the region enclosed by the given curves.

Question

y = 4/x, y = 16x, y =1/4x, x > 0

Find the area.

Answer 1

y = 4/x and y = 16x intersect at (1/2 , 8)
and y = 4/x and y = x/4 intersect at (4,1)

make a sketch and you will see that you have to do it two parts
∫(16x -x/4)dx from 0 to 1/2 + ∫(4/x - x/4)dx from 1/2 to 4

recall that ∫ 1/x dx = ln x

the rest is mostly arithmetic