Suppose that [tex]q(t)[/tex] is the rate at which the temperature of an oven increases in degrees Celsius per minute.

What does the statement [tex]\int_{0}^{20} q(t) \, dt = 120[/tex] mean?

A. It took 120 minutes for the oven to increase 20 degrees Celsius.
B. It took 120 minutes for the oven to decrease 20 degrees Celsius.
C. The oven temperature increased by 120 degrees Celsius in the first 20 minutes.
D. The oven temperature decreased by 120 degrees Celsius in the first 20 minutes.
E. The oven temperature decreased by 120 degrees Celsius in each of the first 20 minutes.
F. The oven temperature increased by 120 degrees Celsius in each of the first 20 minutes.

The statement ²⁰∫₀ q(t) dt = 120 means that the total temperature increase of the oven over the first 20 minutes is 120 degrees Celsius, indicating that the oven's temperature increased by 120 degrees in the given time.

Explanation:

Suppose that q(t) is the rate at which the temperature of an oven increases in degrees Celsius per minute. The statement ²⁰∫₀ q(t) dt = 120 means that the total change in temperature of the oven over the first 20 minutes is 120 degrees Celsius. This is determined by the definite integral, which calculates the area under the curve of the function q(t) from time 0 to 20 minutes, representing the accumulation of temperature change over time.

This integral does not mean it took 120 minutes for the temperature to increase, nor does it imply a temperature increase per minute. Instead, it is simply the total amount of temperature change over those 20 minutes. Hence, the correct interpretation of this statement is Option C: The oven temperature increased by 120 degrees Celsius in the first 20 minutes.