Question

Find an approximate value of `int_1^1.5` x²dx by applying the right–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) = x²

So, the width of each subinterval is

h = Δx

= `("b" - "a")/"n"`

= `(1.5 - 1)/5`

= 0.1

The partition of the interval is given by

x₁ = 1.1

x₂ = 1.2

x₃ = 1.3

x₄ = 1.4

x₅ = 1.5

The right-end rule for Riemann sum with equal width Δx is

S = [f(x₁) + f(x₂) + ….. + f(x_n)]Δx

∴ S = [f(1.1) + f(1.2) + f(1.3) + f(1.4) + f(1.5)](0.1)

= (1.21 + 1.44 + 1.69 + 1.96 + 2.25) × 0.1

= 8.55 × 0.1

= 0.855