QUESTION

Text
Image


The following table shows the $x$ - and $y$-coordinates of five points that lie on a curve $y=f(x)$. \begin{tabular}{|c|c|c|c|c|c|} \hline$x$ & 2 & 2.5 & 3 & 3.5 & 4 \\ \hline$y=f(x)$ & 6 & 4.875 & 4 & 4.125 & 6 \\ \hline \end{tabular} (a) Estimate the area under the curve in the interval $2<x<4$. Use the trapezoidal rule with 4 partitions of equal width. The equation of the curve was found to be $y=x^{3}-7 x^{2}+14 x-2$. (b) (i) Write down an integral that represents the area under the curve over the interval. (ii) Find the exact value of the area under the curve over the interval. (c) Find the percentage error between the estimation in part (a) and the exact value in part (b). Provide a reason for the difference.

Public Answer

RCY3SB The First Answerer