For the function defined on the interval with

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

For the function

f(x)=\dfrac{1}{x^{2}}

defined on the interval

[a,4]

with

a<4

, the average value of

f

over this interval is

\dfrac16

. Determine the value of

a\,.