# Thread: Need help integrating with trig sub

1. ## Need help integrating with trig sub

Problem:

Here is a triangle I have drawn:

Hi I am having a little difficulty figuring out how to solve this problem near the end.

After I used trig sub and integrated it, I get to this point, 20θ + 10sin(2θ). Now at this point I know the θ next to the 20 will be inverse sin(y/2). But figuring out the 10sin(2θ) has gotten me confused. How do we solve for theta in that case?

2. Use the trigonometric identity: $\sin{2\theta} = 2\sin{\theta}\cos{\theta}$.

From your diagram, $\sin{\theta} = \frac{y}{2}$ and $\cos{\theta} = \frac{\sqrt{4 - y^2}}{2}$.

3. Ah I see. Thank you so much!