How do you find the average value of the function for #f(x)=root3(x), 0<=x<=8#?

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Answer 1 · 2017-11-08T09:30:27

#1/(8-0)int_0^8root(3)(x)\ dx=3/2#

The average value of a function #f(x)# from #a# to #b# is given by #1/(b-a)int_a^bf(x)\ dx#.

Just input #f(x)=root(3)(x),a=0,b=8# into the formula: #1/(8-0)int_0^8root(3)(x)\ dx#.

Evaluate this integral using the power rule to get #1/8[3/4x^(4/3)]_0^8#.

This gives #1/8*3/4*8^(4/3)-0=3/2#