# Integral Calculus

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

## Homework Statement

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

## The Attempt at a Solution

$$\int_{0}^{a}\frac{1}{2} (1+cos (2x))$$

$$\frac{x}{2} + \frac{(sin(2x)}{4}$$

$$\frac{a}{2} + \frac{sin(2a)}{4} - 0 - 0 = 0.740$$

$$\frac{a}{2} + \frac{sin(2a)}{4} = 0.740$$

$$2a + sin(2a) = 2.96$$

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

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

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 $$\int_{0 }^{a } cos^2 (x) dx$$. 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. :-/
$$2(1.047) + sin(2(1.047)) = 2.96$$

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