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If the trapezoidal method is used to evaluate the integral obtained $\int_{0}^{1} x^2dx$, then the value obtained

  1. is always > (1/3)
  2. is always < (1/3)
  3. is always = (1/3)
  4. may be greater or lesser than (1/3)
in Numerical Methods by Boss (16.3k points) | 381 views

1 Answer

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Answer is (A)

The approximate value calculated by the trapezoidal method is always greater than the actual value. This can be supported by the argument that value of ERROR= EXACT VALUE- APPROXIMATED VALUE  comes out to be NEGATIVE which shows that approximated value is greater.

by Loyal (7.8k points)
But the given function is strictly decreasing from 0 1o 1 .

can we use this term :"non-monotonically" ??

A function is either "monotonically increasing or strictly increasing or None "

It overestimates the value for all the non-linear curves
yes. I meant that the answer is specific to this question and not applicable for all functions. I don't know exactly which all functions it can be true but I guess it won't be true for any functions which is not monotonically increasing or decreasing.

In the wiki page it is given- overestimate for all concave curves and underestimate for all convex curves.

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