GATE CS 2014 Set 3 Q46 — Numerical Methods (Historical)

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?

1. The value of $K$ obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.
2. The value of $K$ obtained using the Simpson's rule is always equal to the exact value of the definite integral.