How do you calculate the left and right Riemann sum for the given function over the interval [6,8], using n=2 for #f(x) = x^2#?

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Answer 1 · 2017-02-10T16:13:42

See below.

Cut the interval #[6,8]# into #n=2# equal subintervals.

The width (length) of each subinterval will be

#Delta x = (b-a)/n = (8-6)/2 = 1#

The subintervals are #[6,7]# and #[7,8]#

For the left sum, use the left endpoints and add.

#L_2 = f(6)*Deltax + f(7)*Delta x#

# = 36+49 = 85#

For the right sum, use the right endpoints and add.

#R_2 = f(7)*Deltax + f(8)*Delta x#

# = 49+64 = 113#