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Here is the problem: integrate |x minus 1| from 0 to 3.

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Evaluate the definite integral of abs(x minus 1) from x equals 0 to x equals 3.

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Start with the definite integral.

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the integral of |u| du equals u|u|/2.

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Antiderivative.

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Apply the fundamental theorem of calculus.

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So the answer is 5 over 2 approximately 2.5.

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A definite integral gives the signed area between the curve and the x-axis: area above the axis counts as positive and area below counts as negative.

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Differentiated the antiderivative and compared it with the integrand, which checks out.

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Adaptive Simpson prime s rule gives 2.5, which checks out.