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Here is the problem: integral of sqrt(x) from 1 to 9.

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Evaluate the definite integral of sqrt(x) from x equals 1 to x equals 9.

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Start with the definite integral.

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the integral of the square root of x dx equals (2 over 3)x to the power 3 over 2).

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Antiderivative.

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Apply the fundamental theorem of calculus.

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So the answer is 52 over 3 approximately 17.333333.

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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 17.33333333, which checks out.