GATE 2022 MT – Question 61
Estimate the integral of $f(x)=0.2+10x^2$ from 0 to 1 by the single-segment trapezoidal rule: ______ (one decimal place).
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Correct answer: 5.1 to 5.3
Explanation
Endpoint values are $f(0)=0.2$ and $f(1)=10.2$. One trapezoid gives $(1-0)[0.2+10.2]/2=\boxed{5.2}$. This is the numerical estimate requested, not the exact integral.