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Thinking again of the definite integral as an area under a curve, we envision a rectangle whose area is equal to the total area under the curve f(x). The area of that equivalent rectangle is just the length of the integration interval (a,b) times the average value of the integrand over that interval. How to take that average? One way is to sample the integrand at randomly selected points.
a. One dimensional definite integrals
 , where the {xi} form a pseudorandom sequence uniformly distributed in (0,1). Over some other interval,  , where  .
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