Find the area of the region bounded by the graph of F on the X axis on the given interval f(x)=9/x on [-3,-1]

Question

The area of the region is ?

Answer 1

To find the area bounded between the given function f(x) and the x-axis you want to take the integral of the function over the provided interval.

This means here you want to have integral (from x=-3, to x=-1) 9/x

= 9 ln|x| evaluated from x=-3, to x=-1

= 9( ln|-1| - ln|-3|)

= 9 (0 - ln(3))

= - 9 ln(3)

Answer 2

Between x = -3 and x = -1, the graph of f(x) = 9/x lies below the x-axis.

So, area = - ∫ _{(from -3 to -1)} (9/x) dx = - 9ln l x l _{(from -3 to -1)} = -9(ln1 - ln3) = 9ln3