What is the average value of the function g(x)=[x^{2}\sqrt{1=x^{3}}] on

Izabelle Walsh 2022-04-18 Answered
What is the average value of the function g(x)=[x21=x3] on the interval [0,2]?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

xxkrnjangxxed9q
Answered 2022-04-19 Author has 14 answers
If f(x) is a continuous function on the interval [a,b], then the average value is
x=1baabf(x)dx
Here, g(x) is continuous on the interval [0,2]
Therefore, the average value is
x=12002x2+1+x3dx
First, compute the indefinite integral
I=x21=x3dx
Let u=1+x3,,du=3x2dx
Therefore,
I=13u12du=13u3232
=29(1=x3)32+C
And finally
x=1229[(1+x3)32]02
=19((27)(1))
=269
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions