Question

Calculate ∫x²dx, for x ∈ [1, 10] by the Simpson’s rule

Answer 1

For Simpson’s rule take 10 intervals 

Here (b−a)/n = (10−0)/10 = 1 = Δx 

The area under the curve y = x² is given by 

Δx/3(y₀ + 4y₁ + 2y₂ + 4y₃ + 2y₄ +···+ 4y_n−1 + y_n)

The ordinates are found by substituting x = 0, 1, 2 ··· 10 in the equation y = x². Thus 

area = 1/3 (0 + 4 + 8 + 36 + 32 + 100 + 72 +196 +128 + 324 + 100) = 333.3 

In this case Simpson’s rule happens to give exactly the same result as that from direct integration.