How do you estimate the area under the graph of #f(x) = 10sqrt(x)# from #x = 0# to #x = 4# using four approximating rectangles and right endpoints?

1 Answer
Alan P.
Feb 25, 2015

Using equal width rectangles, the 5 sides (remember you need 5 sides for 4 touching rectangles) will occur at
#x=0#, #x=1#, #x=2#, #x=4#, and #x=4#

The right endpoints of the rectangles will have heights"
#f(1) = 10#,
#f(2) = 10 sqrt(2) = 14.14# (approx.),
#f(3) = 10 sqrt(3) = 17.32# (approx.), and
#f(4) = 20#

Since each area has a width of #1# the total area of the #4# approximating rectangles is
#10 + 14.14 + 17.32 + 20#
#= 61.46#
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