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Answer :
Final answer:
The integral of an even function over a symmetric interval is twice the integral over half of that interval. Based on the given information, the integral ∫₀⁷⁰ f(x)dx is equal to -230.
Explanation:
The average value of an even function over an interval is equal to the average value of the function over its entire domain. In this case, the average value of the even function y = f(x) over the interval [-7,7] is given as -115. This means that the average value of y = f(x) over its entire domain is also -115. To find the integral of f(x) from 0 to 70, we use the fact that the integral of an even function over a symmetric interval is twice the integral over half of that interval. So, ∫₀⁷⁰ f(x)dx = 2 * ∫₀⁷ f(x)dx. Since the average value of y = f(x) over its entire domain is -115, the integral ∫₀⁷ f(x)dx is 2 * -115 = -230. Therefore, the correct answer is option c) -230.
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