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Use Simpson's Rule with $ n = 10 $ to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by a calculator.

$ y = xe^x $ , $ 0 \le x \le 1 $

$$\approx 24.145807$$

Applications of Integration

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this question asked us to use Simpson's rule to approximate the area and then compare it with the calculator. What we know we have is we know we're looking at Delta Acts or the with as B minus a one minus zero Divide by End, which is 10 which gives us a 0.1. Now we know our half of axe is gonna be to pie two pi r squared times X plus X squared times square root of two plus four acts plus four X squared We know we're gonna be using Simpsons Rule 0.1, divided by three times F of X zero plus four times affects one plus two times after vexed, too, plus four times off of X three, plus two times f of X four post one times f of x 10 And we know this gives us 13.65 Now we know we're supposed to also be using a calculator so plugged that end directly. There's an integral function. Your calculator pulled this exactly and make sure you have the D of X or whatever you're given. Variable that pops up is is consistent with what your variable is. Over here, we end up with 13.65 so these solutions are both. It's