Aprroximating the area of a surface of revolution using simpsons rule

Question

Consider the surface of revolution generated from rotating the curve $3xe^x$ from $0 leq x leq 1$ about the $x$-axis.
So, the integral will look like:
$$int_0^1 6 pi e^xx sqrt{(3e^xx+3e^x)^2+1} , dx$$
I need to approximate this integral using simpsons rule with $n=10$... After a billion attempts I can't seem to get it right! The correct answer is supposed to be 209.894506
Can somebody walk me through the steps on this one? I feel like i'm going crazy

gt6989b · Accepted Answer

If $n=10$ then $Delta x = (1-0)/10 = 0.1$.
Now
$$
begin{split}
int_a^b f(x) dx
 approx frac{Delta x}{3} left[f(0) + 4f(0.1) + 2f(0.2) \
                                       + 4f(0.3) + 2f(0.4) \
                                       + 4f(0.5) + 2f(0.6) \
                                       + 4f(0.7) + 2f(0.8) \
                                       + 4f(0.9) +  f(1.0)right]
end{split}
$$

Aprroximating the area of a surface of revolution using simpsons rule

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