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Evaluate the integral integral1.24.4 (2x2 + 3x - 1)/(sqrt(x+2)) dx using the Trapezium Rule with eight ordinates.

Mathematics

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To evaluate the integral ∫1.24.42x2+3x−1x+2dx\int_{1.2}^{4.4} \frac{2x^2 + 3x - 1}{\sqrt{x+2}} dx using the Trapezium Rule with eight ordinates, we first need to determine the step width hh.

Step 1: Determine the number of strips (nn) and the step width (hh).
The number of ordinates is given as 8. In the Trapezium Rule, the number of ordinates is typically n+1n+1, where nn is the number of strips.
So, n+1=8  ⟹  n=7n+1 = 8 \implies n = 7 strips.
The limits of integration are a=1.2a = 1.2 and b=4.4b = 4.4.

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