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Georgia Southern University

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Problem 16

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

$$\int_{16}^{25} \int_{2}^{7} \frac{3+5 y}{\sqrt{x}} d y d x$$

Answer

225

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## Discussion

## Video Transcript

Okay, so we're looking in this double in a girl sixteen to twenty five and then Teo seven three plus five. Why over Squared X? Then why the ex? If you recall in problem six, we found this integral as a function of X wass two fifty five over two X to the negative one half. Okay, so this is straightforward. Get was taking anti derivative here. This to fifty five over two is a constant and the next to the one half began except minus one. Happy comes next to the one half divided by one half, evaluated from sixteen to twenty five. So that's because the one half cancels with two multiplied by the reciprocal. You get two fifty five in the times a square, you twenty five minus squared of sixteen, which is five minutes for so that just once and just get to fifty five