Mean value theorem for integration question

[acemi123]

Hello! Can anybody help me with this question?

The function f(x)=x^2 assumes the value of its integral average over the integral [0,3].

a)at point x0=sqrt(3)
b)at point x0=sqrt(5)/2
c)at point x0=sqrt(3)/3
d)at point x0=3/2
e) never on the given interval

I would say 3 with the formula for mean value theorem for integration but I don't see 3 in the answers. What am I doing wrong?

 

[Deleted member 4993]

Hello! Can anybody help me with this question?

The function f(x)=x^2 assumes the value of its integral average over the integral [0,2].

a)at point x0=sqrt(3)
b)at point x0=sqrt(5)/2
c)at point x0=sqrt(3)/3
d)at point x0=3/2
e) never on the given interval

I would say 3 with the formula for mean value theorem for integration but I don't see 3 in the answers. What am I doing wrong?

If you want us to catch/correct your mistake - you'll need to share/show your work. Do your work neatly and post an image - we can go through it and correct it as necessary.

 

[Dr.Peterson]

Hello! Can anybody help me with this question?

The function f(x)=x^2 assumes the value of its integral average over the integral [0,3].

a)at point x0=sqrt(3)
b)at point x0=sqrt(5)/2
c)at point x0=sqrt(3)/3
d)at point x0=3/2
e) never on the given interval

I would say 3 with the formula for mean value theorem for integration but I don't see 3 in the answers. What am I doing wrong?View attachment 25883

You have correctly found the average; but you were asked for the value of x at which f(x) is equal to that average.

Just one little step left!