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Problem 6 Easy Difficulty

Evaluate each integral.
$$\int_{2}^{7} \frac{3+5 y}{\sqrt{x}} d y$$


$\left[\frac{255}{2 \sqrt{x}}\right]$


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Video Transcript

Okay, so here we have this inner girl two to seven of three plus five by divided by Route X. And this is I was respected. Why the wine? Okay, so we're just treating Axis constant. So right off the bat, we can just factor out this one over. Read X. His ex is not changing. It's Spain. Tree is a constantly confected out of the integral. So we just have to seven of three plus five. Why do I We just need an anti derivative, something bad. So we still have one of her rude axe three. Why plus five has why squared Evaluated from to two seven. OK, and so we still have one of her square to vex. And then we'LL just plug in three, Save me of three and then we can just plug in seven minus two again. We can just distribute in this evaluations. I'm just evaluating why it's seven and subtracting evaluating it, too, plus the same thing over here. So this is just seven squared minus two squared. That's forty nine, it's for okay. And so that's one over x. Three times five fifteen. Worse forty nine minus four is forty five and forty five times five is going to be C two twenty five. That's two twenty five over to you or one over X. This's thirty over Tuesday, too. Times two d five over two.