Question on Gauss Quadrature

[adam0sky]

I know the formulae of 2 point gauss quadrature is f(-0.57735)+f(0.57735). Problem is how to use the data to solve the question. I need hints. Many thanks.

 

[HallsofIvy]

??? Where did you get "-0.57735" and "0.57735"? I don't see those numbers anywhere in the given data! And f(-0.57735) and f(0.57735) are not known.

The "Two Point Gauss Quadrature" is a very simple numerical integration method when you are given a number of $\displaystyle (x_i, f(x_i))$ values. It consists of assuming that the function, f(x), is constant from $\displaystyle x_i$ to $\displaystyle x_{i+1}$ so that the "area under the curve" is the area of the rectangle with height $\displaystyle f(x_i)$ and width $\displaystyle x_{i+1}- x_i$, so area $\displaystyle f(x_i)(x_{i+1}- x_i)$.

In this example, you have (x, f(x)) equal to (0, 0), (2, 2.1), (3, 2.9), etc. The first few calculations would be 0(2- 0)+ 2.1(3- 2)+ 2.9(3.8- 3), etc.