Using Trapezoidal rule with h = 0.5 for int_1^3 frac 1 x^2 dx, what is the approximate value?

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SSC Applied Mathematics QUESTION #4167

Question 1

Using Trapezoidal rule with $h = 0.5$ for $\int_1^3 \frac{1}{x^2} dx$, what is the approximate value?

$\frac{1}{2}[f(1) + 2f(1.5) + 2f(2) + 2f(2.5) + f(3)] \times 0.5$
$\frac{1}{2}[f(1) + f(3)] \times 2$
$\frac{0.5}{2}[f(1) + 2f(1.5) + 2f(2) + 2f(2.5) + f(3)]$
Both (A) and (C) are equivalent✔️

Correct Answer Explanation

Trapezoidal rule: $\frac{h}{2}[y_0 + 2y_1 + 2y_2 + 2y_3 + y_4]$. Here $h = 0.5$, so formula is $\frac{0.5}{2}[...] = \frac{1}{4}[...]$, which equals $\frac{1}{2}[...] \times 0.5$.

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