## anonymous 5 years ago a region in the plane is bounded by the graph of y=1/x, the x-axis, the line x=m and the line x=3m, m>0. the area of this region: a) is independent of m b) increases as m increases c) decreases as m increases d) decreases for all m<1/3 e) increases for all m<1/3

1. watchmath

Interesting question! hold on .... :)

2. watchmath

The are of the region is given by $A(m)=\int_m^{3m}\frac{1}{x}\;dx=\int_0^{3m}(1/x)dx-\int_0^m (1/x)dx$ By the fundamental theorem of calculus $A'(m)=\frac{1}{3m}\cdot 3-\frac{1}{m}=0$ So the area doesn't change with respect to m. a) is the answer.

3. anonymous

thanks!:)