Question: Consider the function: f (x) = x 3 (a) Take the integral and calculate ? 1 0 f(x)dx (b) Now consider splitting the interval [0,

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 xi. They may or may not be equally spaced. Calculate the following sums numerically:

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

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

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

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