Consider the function:

f (x) = x³

(a) Take the integral and calculate

?¹₀f(x)dx

(b) Now consider splitting the interval [0, 1] into 4 pieces,

x₀ = 0 x₁x₂x₃x₄ = 1

Where you choose the x_i. They may or may not be equally spaced. Calculate the following sums numerically:

(c) What are the differences between these two sums and how well do they approximate the true value of theintegral?

Transcribed Image Text:

Σια S(x;)(x; - xi-1) f(xi :)(x- x; 1).. i=1