Discussion
The order of magnitude of the error in estimating the value of integral \(\int_{0}^{10}(5x + 6)dx\) numerically using trapezoidal method with a step size of 0.1 is :
Answer: A
The error is 0.
The trapezoidal rule approximates the integrand by a straight line on each sub-interval. Its error term is
\[ E = -\frac{(b - a)h^{2}}{12}f''(\xi) \]
which involves the second derivative. Here f(x) = 5x + 6 is itself linear, so f'' = 0 and the rule is exact apart from rounding, whatever the step size:
\[ \int_{0}^{10}(5x + 6)\,dx = 250 + 60 = 310 \]
The non-zero orders of magnitude in the other options would apply only to an integrand with curvature.
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