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Numerade Educator

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Problem 13 Easy Difficulty

Evaluate each definite integral.
$$\int_{1}^{4} \frac{3}{(3 x+2)^{2}} d x$$

Answer

$\frac{9}{70}$

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Video Transcript

problem. 13 were asked to find this definite in and to do this problem, since it's has, since it has a fraction and a function inside of the function where we're gonna use U substitution and let you equal three X Plus two and we choose this for you because it's a function inside of a square. So if you find the derivative of both sides, you get three d ETS. And this comes out handy because we have a three D X in our originally kitchen so we can go ahead and write this. But before doing that, we have to notice that we have bounds and in the bounds these air expounds We have changed them too. Why bound? And to do that, we just plug it into this equation who, 33 times before plus two to find the upper bound and to find the lower bound we would do three times one plus two. So the upper round is 14 and the lower bound is five. And now we can do the U substitution so would be won over you squared times the u. So this equals you to the minus one over. Now get a one. And you would evaluate this from I to 14. So that just means you have to plug in 14 in replacement of you and then minus Have to plug in five in replacement of you. And this gives us one over 14 minus one word. Negative five. Is this nine over 70?