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}

Answer 1

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.