With respect to the numerical evaluation of the definite integral, \(K = \int…

GATE · 2014 · CS · Set 3 · Computer Science & IT

With respect to the numerical evaluation of the definite integral, \(K = \int \limits_a^b \:x^2 \:dx\), where \(a\) and \(b\) are given, which of the following statements is/are TRUE?

The value of \(K\) obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.

The value of \(K\) obtained using the Simpson's rule is always equal to the exact value of the definite integral.

A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II

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Correct answer: C

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