2

2. What is the average value of xe^x² on the interval [2, 4]?

A. (e¹⁶ - e⁴)/4	B. (e¹⁶ - e⁴)/2	C. (2e¹⁶ - e⁴)/2
D. 2e¹⁶ - e⁴	E. 2e¹⁶ + e⁴

Solution: The answer is A

The average value of a given function f on the interval [a, b] is defined as

So, by definition, the average value of xe^x² on the interval [2, 4] is

Let u = x² thus, ½ du = x dx. Substitute into the above integral.