The trapezoidal rule applied on <msubsup> &#x222B;<!-- ∫ --> 0 <mrow class="MJX-T

The trapezoidal rule applied on ${\int }_{0}^{2}\left[f\left(x\right)\right]dx$ gives the value 5 and the Midpoint rule gives the value $4$. What value does Simpson's rule give?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

First of all,$f\left(1\right)$ should be $2$ since midpoint rule gives you $2f\left(1\right)=4$. You also know that $f\left(0\right)+f\left(2\right)=5$. So
$S=\frac{1}{3}\left[f\left(0\right)+8+f\left(2\right)\right]=\frac{8}{3}+\frac{1}{3}\cdot 5=\frac{13}{3}$