# Thread: Ηelp for definite integral

1. ## Ηelp for definite integral

Ηelp for definite integral

2. ## Re: Ηelp for definite integral

$\displaystyle V^2=\frac{1}{2\pi}\left \{\int_{0}^{\pi} \eta \mu^2 (vt)d(vt)\right \}^{\frac{1}{2}}$

Calculating the integral gives us:
$\displaystyle \int_{0}^{\pi} \eta \mu^2 (vt)d(vt)\right = \eta \mu^2 \int_{0}^{\pi} (vt)d(vt) = \eta \mu^2\left[\frac{(vt)^2}{2}\right]_{0}^{\pi} = \eta \mu^2\left(\frac{\pi^2}{2}\right)$

The answer should be clear now.

3. ## Re: Ηelp for definite integral

Siron,

I' m sure that what you wrote me does not hold. It is not allowed to seperate sin^2 from (ut), because sinf(x) is a function.

I appreciate your taking the time to write to me but it would be better not to help, if you do not know.

M.

4. ## Re: Ηelp for definite integral

Perhaps it would help if you told us what in the world you are talking about! There is no "sin" or "sinf" in the attached file.

5. ## Re: Ηelp for definite integral

You are right. Sorry.

6. ## Re: Ηelp for definite integral

power reduction identity ...

$\displaystyle \sin^2{u} = \frac{1-\cos(2u)}{2}$

... so do it.

7. ## Re: Ηelp for definite integral

Is it possible for you to write me the hole solution because I have a doubt for one point of the procedure?

8. ## Re: Ηelp for definite integral

Originally Posted by mbempeni
Is it possible for you to write me the hole solution because I have a doubt for one point of the procedure?

Write down the procedure you attempted, then someone may comment on whether the procedure you followed is correct ... or not.

9. ## Re: Ηelp for definite integral

I' ve just done it!

10. ## Re: Ηelp for definite integral

$\displaystyle u = \omega t$

$\displaystyle \int_0^\pi \sin^2{u} \, du$

$\displaystyle \frac{1}{2} \int_0^\pi 1 - \cos(2u) \, du$

$\displaystyle \frac{1}{2} \left[u - \frac{\sin(2u)}{2} \right]_0^\pi$

$\displaystyle \frac{1}{2} \left[\left(\pi - 0 \right)-\left(0-0\right)\right] = \frac{\pi}{2}$