PYQs Based Test - 27 : Numerical Methods (Integral Equations)

Match the CORRECT pairs:

With respect to the numerical evaluation of the definite integral. $K={\int }_a^b{x}^{2}dx,$ where a and b are given, which of the following statements is/are TRUE?

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

II) The value of K obtained using the Simpson’s rule is always equal to the exact value of the definite integral.

The definite integral $\underset{1}{\overset{3}{\int }}\frac{1}{x}dx$ is evaluated using Trapezoidal rule with a step size of 1. The correct answer is __________

Using the Simpson’s 1/3rd rule, the value of ∫ydx computed, for the data given below, is ________.

Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral $\underset{-1}{\overset{+1}{\int }}\left|x\right|dx$ is _____