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The temperature in a room at midnight is 20 degrees Celsius. Over the next 24 hours, the temperature changes at a rate modeled by the differentiable function H, where H(t) is measured in degrees Celsius per hour and time t is measured in hours since midnight. Which of the following is the best interpretation of 0 6 H(t) dt?
(A) The temperature of the room, in degrees Celsius, at 6:00 A.M.
(B) The average temperature of the room, in degrees Celsius, between midnight and 6:00 A.M.
(C) The change in the temperature of the room, in degrees Celsius, between midnight and 6
(D) The rate at which the temperature in the room is changing, in degrees Celsius per hour, at 6:00 A.M.

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facundo3141592

It will represent the change in temperature between midnight and 6, the correct option is C.

Which is the best interpretation of ∫H(t)*dt?

H(t) is the rate at which the temperature changes. So, if we integrate H(t), we will get the change of temperature.

In this case, we have:

[tex]\int\limits^6_0 {H(t)} \, dt[/tex]

This will give the change in temperature between 6:00 AM (represented by the 6) and midnight (represented with the 0).

So the correct option is C.

If you want to learn more about integration, you can read:

https://brainly.com/question/18760518