# Thread: Integral Mean Value Theorem

1. ## Integral Mean Value Theorem

Can someone show me how to do this... Find a value o c that satisfies the conlusion of the Integral Mean Value Theorem.

3X^2(=8) on [0,2]

I know the answer is 2/squareroot(3), and it is solved by the quadratic formula, but do not know how to get that.

I also know that f(C)=4 OR 3C^2 = 4.

2. Originally Posted by gammaman
Can someone show me how to do this... Find a value o c that satisfies the conlusion of the Integral Mean Value Theorem.

3X^2(=8) on [0,2]

I know the answer is 2/squareroot(3), and it is solved by the quadratic formula, but do not know how to get that.

I also know that f(C)=4 OR 3C^2 = 4.
You need $\displaystyle f(c) = \frac{1}{2-0}\int_0^2 3x^2 dx$
Therefore, $\displaystyle 3c^2 = \frac{1}{2}\int_0^2 3x^2 dx$

Now solve for $\displaystyle c$ after evaluating the RHS.

3. Ok but how do I get the answer?

4. Originally Posted by gammaman
I thought that would be solving using the Integral Mean Value Theorem? I want to know how to get the value for c.
That is exactly how you get that number. After you evaluate the integral on the RHS you get a number and so you have $\displaystyle 3c^2 = \text{number}$. This is an equation of $\displaystyle c$ and so you can solve this equation for $\displaystyle c$.

Solving $\displaystyle 3 c^2 = \text{number}$ using the quadratic equation is like killing a fly with an elephant gun.