Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ).

$$\int_{0}^{3} \int_{1}^{2}\left(x y^{3}-x\right) d y d x$$

$\frac{99}{8}$

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Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Okay, so now we have this double inner girl. So we're going to first integrate with respect to one variable and then the second variable, uh, X, Why minus X and then divide E X. But actually in problem too. We actually evaluated this inner integral as a function of X. So if your call or you can just go back and look at that problem, you just take an anti derivative with respect to why? And then evaluate it too. You get eleven fourths x. So that's what this becomes here and now you just take this is just a standard anti derivative of dysfunction and then evaluated the end points Fundamental theorem of calculus. So we have eleven over eight X squared X crater, two tonnes. Blood number four I rated from zero to three. But this is okay. So x squared three squared is mine. So just ninety tien over a minus. Yeah,

Georgia Southern University