How do you calculate the left and right Riemann sum for the given function over the interval [1,5], using n=4 for f(x)= 3x?

1 Answer
Mar 5, 2017

LRS = 30
R RS = 42

Explanation:

We have:

f(x) = 3x

We want to calculate over the interval [1,5] with 4 strips; thus:

Deltax = (5-1)/4 = 1

Note that we have a fixed interval (strictly speaking a Riemann sum can have a varying sized partition width). The values of the function are tabulated as follows;

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Left Riemann Sum

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LRS = sum_(r=1)^4 f(x)Deltax
" " = Deltax { f(1) + f(2) + f(3) + f(4) } \ \ \ (The LHS values)
" " = 1*(3+6+9+12)
" " = 30

Right Riemann Sum

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R RS = sum_(r=2)^5 f(x)Deltax
" " = Deltax { f(2) + f(3) + f(4) +f(5) } \ \ \ (The RHS values)
" " = 1*(6+9+12+15)
" " = 42

Actual Value

For comparison of accuracy:

Area = int_1^5 \ 3x \dx
" " = 3[x^2/2]_1^5
" " = 3/2{(25)-(1)}
" " = 36