Triangle that has the hypo as √(u^2 +1)

Homework Statement

If I have a triangle that has the hypo as √(u^2 +1)
adj as 1 and oppo as u
I did an integral with trig sub. So I used

u = tan(θ)

The Attempt at a Solution

At the end of my integral I ended up with an expression (1/4)sin(2θ)
When I substitute back in to the integral for theta. I will get (1/2)(u/(sqrt(u^2 +1))
right? How does back sub work if you have 2(theta)

vela
Staff Emeritus
Homework Helper
Use ##\sin 2\theta = 2 \sin \theta \cos \theta##. You need the trig functions in terms of ##\theta##, not ##2\theta##.

Always like this? With double angle?

vela
Staff Emeritus