The average value of y = h(x)equals a for 0 $\le$x $\le$ 5, and equals b for 5 $\le$ x $\le$ 15.What is the average value of h(x)for 0 $\le$ x $\le$ 15?
A) $\frac{a+b}{2}$
B) $\frac{a+2 b}{3}$
C) $\frac{a+b}{15}$
D) $\frac{a+2 b}{15}$

Question

Quizplus · Accepted Answer

The average value of $h(x)$ over the interval from 0 to 15 can be calculated by taking the weighted average of the two segments (0 to 5 and 5 to 15) since the function has different average values ($a$ and $b$) over these intervals. The first segment is 5 units long and has an average value of $a$, while the second segment is 10 units long (twice as long as the first) and has an average value of $b$. Therefore, the overall average is weighted more towards $b$, resulting in $\frac{a+2b}{3}$.

The Average Value of Y = H(x)equals a for 0 ≤\le≤

The Average Value of Y = H(x)equals a for 0 $\le$