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Numerade Educator

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Problem 28 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int^{2}_{1} \biggl( \frac{1}{x^2} - \frac{4}{x^3} \biggr) \,dx $

Answer

$-1$

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Video Transcript

We're looking at the integral from 1-2 of this function one over x squared Uh -4 over x cubed dx. And before doing the anti direct of what I would do is rewrite this is X to the name of second power minus four X. To the negative third power dx. And now we can follow our rules where we add one to the exponents. Now we multiply by the reciprocal of that new experiment. Just remember that when you add to a negative uh A lot of students make that mistake where adding 12 negative three, they write negative four, but negative three plus one is negative two. And when you divide negative forward by negative two, you get a positive too From 1- two. Um And it might be worth your while to remember that this is equal to negative one over X plus two over X squared From 1- two. But sometimes I don't even do that because I don't know, it just makes sense in my head to leave this alone. Uh When you plug into and for X. Squared, you get to force or one half. Um So that's actually zero. But then when you have to plug in, your lower balance would be negative one plus two. Um so you get one there but remember it's a negation of that value, so it should be negative one as your final answer. So let's circle that and move on. Okay.