What is the average value of the function #f(x)=3x^2-4# on the interval [ 2, 6]?
Find the average value of the function #f(x)=3x^2-4# on the interval [ 2, 6]
Find the average value of the function
1 Answer
May 29, 2018
Explanation:
Remember, the average value of a function is given by
#color(blue)(f_(avr)=1/(b-a)int_a^bf(x)dx#
For your problem
#f_(avr)=1/(6-2)int_2^6 3x^2-4dx#
#color(white)(f_(avr))=1/4int_2^6 3x^2-4dx#
Integrate by the power rule
#f_(avr)=1/4[(x^3-4x)]_2^6#
#color(white)(f_(avr))=1/4((6^3-4*6)-(2^3-4*2))#
#color(white)(f_(avr))=1/4*192#
#color(white)(f_(avr))=48#