Posted by **Mark** on Tuesday, December 1, 2009 at 3:00am.

a) Suppose f(x) is defined on 0 ≤x≤1 by the following rule: f(x) is the first digit in the decimal expansion for x. For example, f(1/2) = 5 and f(0.719) = 7. Sketch the graph of y = f(x) on the unit interval with appropriate scales for x and for y. Use a graphical interpretation of the definite integral to compute ∫_0^1▒f(x)dx.

b) Suppose the function g(x) is defined as follows: g(x) is the second digit in the decimal expansion for x. For example, g(0.437) = 3. Compute ∫_0^1▒g(x)dx. Use graph.

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