Water flows into an empty reservoir at a rate of $3400+15 t$ gal/hour. What is the quantity of water in the reservoir after 10 hours? Answer: gallons.

Step 1 ：The rate at which water is flowing into the reservoir is given by the function \(3400+15t\).

Step 2 ：To find the total quantity of water after 10 hours, we need to integrate this function from 0 to 10.

Step 3 ：The result of the integration is 34750.

Step 4 ：This means that after 10 hours, there will be 34750 gallons of water in the reservoir.

Step 5 ：Final Answer: The quantity of water in the reservoir after 10 hours is \(\boxed{34750}\) gallons.