- #1

Gyroscope

## Homework Statement

[tex]\Delta s=\int^{t_f}_{t_0}\sqrt{v_0^2-2v_0\sin\theta gt+g^2t^2}~dt[/tex]

Can someone tell me how to integrate this? I am just an high-school sutdent and have basic integration knowledge.

Thanks in advance.

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- Thread starter Gyroscope
- Start date

- #1

Gyroscope

[tex]\Delta s=\int^{t_f}_{t_0}\sqrt{v_0^2-2v_0\sin\theta gt+g^2t^2}~dt[/tex]

Can someone tell me how to integrate this? I am just an high-school sutdent and have basic integration knowledge.

Thanks in advance.

- #2

AlephZero

Science Advisor

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Do you know how to do integrals containing [tex]\sqrt{a^2 + x^2}[/tex]?

If so, you can get it into that form by "completing the square":

[tex]g^2t^2 - 2v_0 \sin\theta gt + v_0^2[/tex]

= [tex](gt - v_0 \sin\theta)^2 + \dots[/tex]

Then substitute [tex] u = gt - v_0 \sin\theta[/tex]

- #3

Gyroscope

- #4

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- #5

Gyroscope

Are you sure it is integration by parts?

- #6

AlephZero

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[tex]\int{\frac{1}{\sqrt{1+x^2}} = \sinh^{-1}x[/tex]

and integration by parts should get you there.

If you just want the answer (e.g. to use in a project on the motion of projectiles, or whatever) go to http://integrals.wolfram.com/index.jsp

- #7

Gyroscope

I have just studied this functions the last hours and the inverse integration by substitution. I am just an high-school student but I have a calculus book, from where I am studying, it gives a good preparation for IPHO. I am now going to see integration by parts and how to apply in this situation.

Thank you very much Aleph for helping me.

Thank you very much Aleph for helping me.

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