Question

How do you estimate the area under the graph of `f(x)= 2/x` on [1,5] into 4 equal subintervals and using right endpoints?

Answer 1

Use `f(x_1)*Deltax+ f(x_2)*Deltax+ f(x_3)*Deltax+ f(x_4)*Deltax`

Explanation:

Cut `[1,5}` into 4 subintervals of equal length
`Delta x = (b-a)/n = (5-1)/4 = 1`

The endpoints of the subintervals are:
`x_i = a+iDeltax` for `i = 0,1,2,3, . . . ,n`

In this question the subintervals are:

`[1,2]`, `[2,3]`, `{3, 4]`, [4,5]# and the RIGHT endpoints are:

`2, 3, 4, "and "5`

The heights at the endpoints are:

`f(2) = 2/2=1`

`f(3) = 2/3`

`f(4) = 2/4 = 1/2`

`f(5) = 2/5`

So the area is approximately:

`1*1+2/3*1+1/2*1+2/5*1 = 77/30`