Find the average value of the function over the given interval.
-f(x) = 7 - x on [-7, 7]
A) 49
B) $\frac { 7 } { 4 }$
C) $\frac { 7 } { 2 }$
D) 7

Question

Find the average value of the function over the given interval.
-f(x) = 7 - x on [-7, 7] 
A) 49
B) $\frac { 7 } { 4 }$
C) $\frac { 7 } { 2 }$
D) 7

Quizplus · Accepted Answer

To find the average value, we need to use the formula:

Average value = (1/(b-a)) * ∫[a to b] f(x) dx

Plugging in the given values, we get:

Average value = (1/(7-(-7))) * ∫[-7 to 7] (7-x) dx

= (1/14) * [(7x - (x^2)/2) from -7 to 7]

= (1/14) * [(49 - 49/2) - (-49 + 49/2)]

= (1/14) * [(49/2) + (49/2)]

= 7/2

Therefore, the best choice is C, which is 7/2.

Find the Average Value of the Function Over the Given 74\frac { 7 } { 4 }47​