13. What is the average value of the function f(x) = x sin(x2) over the interval [2,4]?
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A. sin 4 + 2 sin 16 |
B. –sin 4 + 2 sin 16 |
C. (cos 4 – cos 16)/2 |
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D. (cos 4 – cos 16)/4 |
E. (-cos 4 + cos 16)/4 |
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Solution: The answer is D
The average value of the function f(x) = x sin(x2) over the interval [2,4] is given by integrating f(x) over the same interval and dividing by the length of the interval. That is,
Consequently,
