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Math Help - Need help integrating with trig sub

  1. #1
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    Question Need help integrating with trig sub

    Problem:
    Need help integrating with trig sub-w0p8d4.png

    Here is a triangle I have drawn:
    Need help integrating with trig sub-123uopk.png

    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?
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  2. #2
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    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}.
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  3. #3
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    Ah I see. Thank you so much!
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