Answer true of false: The average value of f(x) = 5x⁹ on the interval [-5, 5] is 0.

Question

Quizplus · Accepted Answer

To find the average value of a function on an interval, we use the formula (1/(b-a)) * definite integral from a to b of f(x) dx. In this case, a = -5 and b = 5. Evaluating the definite integral, we get: (1/(5-(-5))) * definite integral from -5 to 5 of 5x⁹ dx = (1/10) * [((5x^2)/2) - ((-5x^2)/2)] evaluated from -5 to 5 = (1/10) * [(50/2) - ((-50)/2)] = (1/10) * 50 = 5 Therefore, the average value of f(x) on the interval [-5, 5] is 5, not 0.

Answer True of False: the Average Value of F(x) =