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Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

$ y = xe^{-x} $, $ 0 \le x \le 2 $

$L=\int_{0}^{2} \sqrt{1+(x-1)^{2} e^{-2 x}} d x \approx 2.1024$

Applications of Integration

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so we have to find the length of the curve. Why equals X E to the negative X on the interval? X is greater than or equal to zero, but less than or equal to two. So first we'll find the derivative of why, so that we can plug that into our our clean formula. So that will be our derivative and given the interval, are a will equal zero and bebel equal to radical one. Plus, he'd the negative x minus x times each The negative x squared T X will go to the next page. And the problem asked us to use a calculator. So we'll want to simplify. Um, our expression under the radical A bit, um, so that plugging it into the calculator will be a bit easier. Um, here we can expand the expression under the radical Um, excuse me. Getting X minus one squared times e to the negative to x. So that was plus one under the radical T X. After plugging this into your calculator, you should get around 2.10 to 4