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The trapezoidal rule applied on $ \int_0^{2} [f(x)] dx$ gives the value 5 and the Midpoint rule gives the value 4. What value does Simpson's rule give?

So we have that T=f(0)+f(2).

The Simpson's value is S=(1/3)*(f(0) + 4f(1)+ f(2))

f(1) here is equal to 4 since its the midpoint value.. I dont how how to combine these together to find the simpson's value

user3543012
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1 Answers1

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First of all, $f(1)$ should be $2$ since midpoint rule gives you $2f(1)=4$. You also know that $f(0)+f(2)=5$. So

$S=\frac{1}{3}[f(0)+8+f(2)]=\frac{8}{3}+\frac{1}{3}\cdot5=\frac{13}{3}$.

KittyL
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