calculus 2

Question

y = 4/x, y = 4/x2, x = 6

 

find the area

Answer 1

The curves intersect when x=1.

 

Between x=1 and x=6 the graph of y=4/x lies above the graph of          y = 4/(x²)

 

Area between the curves = ∫_{(from 1 to 6)}[4/x - 4/(x²)]dx

 

                                   = 4(lnlxl + 1/x)_{(from 1 to 6)}

 

                                   = 4[(ln6 + 1/6) - (ln1 + 1)]

 

                                   = 4ln6 - 10/3 ≈ 3.83