Final answer:
To find the average value of the function y = 6 - x^2 over the interval [-5,2], calculate the definite integral over that interval and then divide by the length of the interval. After computing, the average value is approximately 11.57.
Step-by-step explanation:
The question asks us to find the average value of the function y = 6 - x2 over the interval [-5,2]. To do this, we'll use the formula for the average value of a continuous function over a closed interval [a,b], which is (1 / (b - a)) × ∫ab f(x) dx. This translates into dividing the definite integral of the function over the interval [a,b] by the length of the interval.
Firstly, we calculate the length of the interval, which is (2 - (-5)) = 7. Next, we calculate the definite integral of the function from -5 to 2:
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To find the average value, divide the integral result by the length of the interval:
Average value = (1/7) * 81 = 11.57 (approximately, up to two decimal places).
Therefore, the average value of the function y = 6 - x2 over the interval [-5,2] is approximately 11.57.