Question

Approximate the area under the curve of y = 1/x and above the x-axis from x = 1
to x = 2 by using a left sum with five subintervals
of equal length. Will this be an under, or
over-approximation to the actual area under the curve? Please explain.

Answer 1

to answer the second question first, my drawing showing two subintervals shows that this will be an over-approximtion to the actual area under the curve

Answer 2

ok got that part

Answer 3

each subinterval will have a width of (2-1)/5=1/5
we have:\[A \approx f(1)\Delta x+ f(1.2)\Delta x + f(1.4) \Delta x + f(1.6) \Delta x + f(1.8) \Delta x\]where delta x=1/5

Answer 4

\[A \approx (\frac{1}{1}+\frac{1}{1.2}+\frac{1}{1.4}+\frac{1}{1.6}+\frac{1}{1.8})\frac{1}{5}\]Do the computation and there you go :)

Answer 5

got it.