Integral Mean Value Theorem

**gammaman** · February 15th 2009, 01:14 PM

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.

**ThePerfectHacker** · February 15th 2009, 01:22 PM

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 $f(c) = \frac{1}{2-0}\int_0^2 3x^2 dx$
Therefore, $3c^2 = \frac{1}{2}\int_0^2 3x^2 dx$

Now solve for $c$ after evaluating the RHS.

**gammaman** · February 15th 2009, 01:25 PM

Ok but how do I get the answer?

**ThePerfectHacker** · February 15th 2009, 01:28 PM

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 $3c^2 = \text{number}$ . This is an equation of $c$ and so you can solve this equation for $c$ .

**gammaman** · February 15th 2009, 01:29 PM

But what about the quadratic equation? Do I need that?

**mr fantastic** · February 15th 2009, 05:56 PM

Originally Posted by gammaman

But what about the quadratic equation? Do I need that?

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

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