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Problem 40 Medium Difficulty
The table shows values of a force function $ f(x) $, where x is measured in meters and $ f(x) $ in newtons. Use Simpson's Rule to estimate the work done by the force in moving an object a distance of 18 m.
Answer
148 $\mathrm{J}$
Topics
Integration Techniques
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Video Transcript
Okay, so this question wants us to estimate the work done, which is given by the integral under a force distance graph. So it wants us to use Simpson's role. So to figure out how many sub intervals we need let's look at how many data points were given. So were given seven data points. So our end is data points minus one. So it's six and then to find our Delta X be minus a over end, which is, well, we're ending at 18 and we're starting at zero, and we got six some intervals, so Delta X should be three. So now we get S of six is approximately equal to the world. So s of six is Delta X over three, which is three divided by three. So it's just one times f of zero plus four times f of three plus two times f of six plus all the way up to s of 18. And then just using the values that we know from the table, we can see that the work is approximately 148 Jules and again, all we do is plugging the values from the table injury to the efs remembering the alternate, the fours and the twos. Except for the end points, of course, and we'll get an answer of 1 48 Jules.
University of Michigan - Ann Arbor
Topics
Integration Techniques
Top Calculus 2 / BC Educators
Anna Marie V.
Campbell University
Heather Z.
Oregon State University
Caleb E.
Baylor University
Kristen K.
University of Michigan - Ann Arbor