Final answer:
The average value of f(x) = 4x⁴ over [1,3] is 1023/4.
The correct option is a) 1023/4.
Step-by-step explanation:
To find the average value of the function f(x) = 4x⁴ over the interval [1,3], we need to evaluate the definite integral of f(x) over that interval and divide it by the length of the interval. The average value is given by:
Average value = (1/3-1) * ∫[1,3] 4x⁴ dx
Integrating the function f(x), we get:
Average value = (1/3-1) * [x⁵] from 1 to 3
Plugging in the upper and lower limits into the antiderivative, we get:
Average value = (1/3-1) * [(3)⁵ - (1)⁵]
Average value = (1/3-1) * (243 - 1)
Average value = 1023/4
The correct option is a) 1023/4.