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Question
Find an approximate value of `int_1^1.5` xdx by applying the left–end rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}
Solution
Here a = 1
b = 1.5
n = 5
f(x) = x
So, the width of each subinterval is
h = `Deltax = ("b" - "a")/"n"`
= `(1.5 - 1)/5`
= `0.5/5`
= 0.1
x0 = 1
x1 = 1.1
x2 = 1.2
x3 = 1.3
x4 = 1.4
x5 = 1.5
The left hand rule for Riemann sum,
S = [f(x0) + f(x1)) + f(x2) + f(x3) + f(x4)]∆x
= [f(1) + f(1.1) + f(1.2) + f(1.3) + f(1.4)](0.1)
= [1 + 1.1 + 1.2 + 1.3 + 1.4](0.1)
= [6](0.1)
= 0.6.
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