What is the average value of a function y=50x+5 on the interval [3, 9]?

Question

tennispopj8 · Accepted Answer

The average value of a function f(x) on the interval [a,b] is given by:
average value

= \frac{1}{b - a} \int_{a}^{b} f (x) d x

So here, the average value is:

\frac{1}{9 - 3} (50 x + 5) d x

= \frac{5}{6} \int_{3}^{9} (10 x + 1) d x

Integrating term by term:

= \frac{5}{6} [5 x^{2} + x]_{3}^{9}

= \frac{5}{6} [(5 (9)^{2} + 9) - (5 (3)^{2} + 3)]

= \frac{5}{6} (414 - 48)

=305

Erin Lozano · Accepted Answer

Use the average function   a  v  g  =      1          b      −      a            ∫          a              b        f  (  x  )  d  x  a  v  g  =      1          9      −      3            ∫          3              9        (  50  x  +  5  )  d  x  =      1    6        ∫          3              9        (  50  x  +  5  )  d  x  a  v  g  =      1    6    [            50              x                  2                      2    +  5  x      ]          3              9        =      1    6    [  25      x          2        +  5  x      ]          3              9        a  v  g  =      1    6    [  (  25  ∗  9  +  5  ∗  9  )  −  (  25  ∗      3          2        +  5  ∗  3  )  ]  a  v  g  =      1    6    (  2070  −  240  )avg=305

What is the average value of a function y=50x+5 on

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