smc-5196-10-Trapezium rule

The algorithm below, described in pseudocode, estimates the value of a definite integral using the trapezium rule.

Consider the algorithm implemented with the following inputs.

The value of the variable sum after one iteration of the while loop would be closest to

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\(C\)

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\((f(x), a, b, n)\ \rightarrow\ (\log_{e}x, 1, 3, 10) \)

\(h=\dfrac{b-a}{n}=\dfrac{3-1}{10}=\dfrac{1}{5}\)

\(\text{Sum}=f(a)+f(b)=\log_{e}1+\log_{e}3=\log_{e}3\)

\(\text{1st iteration of}\ \textbf{while }\text{loop:}\)

\(x\)	\(=a+h=1+\dfrac{1}{5}=\dfrac{6}{5}\)
\(\text{Sum}\)	\(=\text{Sum}+2\times f(x)\)
	\(=\log_{e}3+2\times f\Bigg(\dfrac{6}{5}\Bigg)\)
	\(=\log_{e}3+2\times \log_{e}{\Bigg(\dfrac{6}{5}\Bigg)}\)
	\(\approx 1.46325\dots\)

\(\Rightarrow C\)