Determine whether the statement is true or false, and explain why.
the average value of the function f(x) =2x2+3 on [1,4] is given by
1/3∫^4_1π(2x^2+3)^2 dx.

False

Step-by-step explanation:

The statement is False, because the average value of a funciton f(x) on an interval is given by the value of the integral of the function on that interval divided by its length. In this case, the integral is right, but we are not integrating exactly f, and thats why the average value is not given correctly.