Find the area of the region

Question

y = 4/x,  y = 4/x²,  x = 6

Find the area of the region: _______

Answer 1

f(x) = 4/x and g(x) = 4/x^2

their integral are F(x) = 4 ln|x| and G(x) = -4/x

they intersect at 4/x = 4/x^2

4x = 4

x= 1

they intersect at (1,4)

from 1 to 6, f(x) is on top, so

4 ln 6 + 2/3 - (0 - -4) =

4 ln 6 + 2/3 - 4

= 4 ln 6 - 10/3

for x=0 to 1, integrates with respect to y-axis instead

Finv = 4/y

Ginv = 2/sqrt(y)

and limits become y=4 to infinity with g(x) on top

lim y-->4 is zero

as y-->infinity the limit is zero

so nothing becomes of this limit

There's the area: 4 ln 6 - 10/3