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Problem 15

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

$$\int_{1}^{2} \int_{4}^{9} \frac{3+5 y}{\sqrt{x}} d x d y$$

Answer

21

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## Discussion

## Video Transcript

We're looking at the iterated integral of three plus five. Why over square root x dx dy y the bounds on the inter Girls are 1 to 2 and 4 to 9 Because the D X is listed first. That means we're looking at this inner integral first with respect to X Treating. Why is constant? This is problem five from the same section and the answer is six plus 10. Why? So this is what's inside the why into girl. So we're looking at the integral from 1 to 2 of six plus 10 y. Do you? Why, this is just an integral in one variable. So the anti derivative is six y plus five y squared evaluated from 1 to 2. So we plug into that six times two plus five times two squared and we subtract the results from plugging and one which is six times one plus five times one squared. That's 32 12 plus 20 minus six plus five, which is 11. The final answer is 21

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