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

$$\int_{1}^{5} \int_{2}^{4} \frac{1}{y} d x d y$$

2 $\ln 5$

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All right, here we have these double integral here. One, two, five and then Teo for of one over. Why d x y Okay, so anti derivative of this will. Actually, we can factor out the one over five. You know, I wonder if I wonder why we just have the inner girl from two to four d X But this is just a rectangle, right? This is just like integrating the constant function of one. So we just take the difference of the inquest. So that's two. So you get a factor of two Integrate One defies one over Why? Bye Anti derivative of one over. Why his natural log? Absolute value of why I rated from one to five citizens too natural. Five minus well to national. I'll have one with that. Syria. So there's your answer

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