# Integration with a square root

## Homework Statement

The problem is really about finding the length of a parametrically defined curve, this in itself seems easy enough, but it's the integration part that's hard.
The problem is as follows:
x = cost
y = t + sint
t = 0.....pi

## The Attempt at a Solution

So in order to find the length of this curve I need to find the integral from 0 to pi of:
sqrt((dy/dt)^2 + (dx/dt)^2)
dy/dt = 1 + cost
dx/dt = -sint

So I get the integral of:
sqrt((-sint)^2 + (1+cost)^2)) =
sqrt((sint)^2 + (cost)^2 + 2cost + 1)
(sint)^2 + (cost)^2 = 1, so I get the integral of:
sqrt(2+2cost).

And to be quite frank this has left me completely stumped. Googling around the internet I've read some stuff about trigonometric integration but there's nothing in the whole book about this, so I doubt that's how I'm supposed to solve it. I'm thinking I might be supposed to find a way to rewrite 2+2cost so that I can integrate but it has been to no avail.

A push in the right direction would definately be appreciated.

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Dick
you can use the double-angle formula: $$\cos^2 t=\frac{1+\cos 2t}{2}$$