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?

1 Answer
Aug 12, 2015

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#