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Problem 2 Easy Difficulty

Evaluate each integral.
$$\int_{1}^{2}\left(x y^{3}-x\right) d y$$


$=\frac{11}{4} x$


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Video Transcript

Okay, so you don't evaluate this integral of a function of two variables. So you go from one to two of next. Why? Cute minus X do you want? So we're evaluating this, Integral with respect. Why on we're treating exes if expert just a constant. Okay, so the final answer will actually be a function of X. So we need to take an anti derivative of this grand with respect of why so have X. Why did the fourth of before thanks for the stream like a constant minus x y. And then we evaluate this from one to two. So you're finally answerable. Plug in two for why this is Y equals two and Michael Spine. So that's going to be eight over. Let's see to the fourth at sixteen. So for X minus two x, okay. And then that's evaluated it, too. And then minus We'LL have X over for minus It's X. Okay. And so this is two x minus. This is going to be negative. Three fourth ex said to X is like eight Exeter for plus three Exeter, for that's gonna be eleven words. Next