Final Answer:
A) The area under the curve can be determined using a single definite integral because The definite integral allows us to calculate the area between the curve and the x-axis within the given interval.
Step-by-step explanation:
To find the area under the curve y = f(x) for x ∈ [0, 7π], we can use a single definite integral. The definite integral allows us to calculate the area between the curve and the x-axis within the given interval.
By integrating the function f(x) with respect to x over the interval [0, 7π], we can determine the area under the curve. The definite integral represents the accumulation of infinitely many infinitely small areas, resulting in the total area.
The definite integral of f(x) over the interval [0, 7π] is denoted as ∫[0, 7π] f(x) dx. This integral represents the area under the curve between x = 0 and x = 7π.
By evaluating this definite integral, we can find the exact numerical value of the area under the curve. The result will depend on the specific function f(x) and its behavior within the given interva
Therefore, the correct answer is A) The area under the curve can be determined using a single definite integral.