Solve Integral Calculus: Find a Value for a

[planauts]

Hi, I have another question that I am having trouble with:

Homework Statement

Find the value of a such that:
[tex]\int_{0 }^{a } cos^2 (x) dx[/tex]

The Attempt at a Solution

[tex]\int_{0}^{a}\frac{1}{2} (1+cos (2x))[/tex]

[tex]\frac{x}{2} + \frac{(sin(2x)}{4} [/tex]

[tex]\frac{a}{2} + \frac{sin(2a)}{4} - 0 - 0 = 0.740[/tex]

[tex]\frac{a}{2} + \frac{sin(2a)}{4} = 0.740[/tex]

[tex] 2a + sin(2a) = 2.96[/tex]

I am stuck after this...How would I solve the trig equation?

Maybe...[tex] m + sin(m) = 2.96[/tex]
where m = 2a
But I don't think that will get me anywhere :-/

Thanks for your help!

 

[AfterSunShine]

This equation can not b solved elementary.
Did you post the whole question?
Also, your question isn't complete. Such the integral equal what?

 

[planauts]

This equation can not b solved elementary.
Did you post the whole question?
Also, your question isn't complete. Such the integral equal what?

This is what the question says:

Find the value of a such that [tex] \int_{0 }^{a } cos^2 (x) dx
[/tex]. Give your answer to 3 decimal places.

The answer is: a = 1.047

EDIT:
The answer does work but I don't know how my teacher got it. :-/
[tex]
2(1.047) + sin(2(1.047)) = 2.96
[/tex]

 

[fzero]

I would use Newton's method to find the numerical value of the root of [tex]
2a + sin(2a) = 2.96
[/tex].