## anonymous 3 years ago verify my trigonometric substitution

1. anonymous

integral of ((sqrt(4-x^2)/x^2)dx

2. anonymous

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3. anonymous

|dw:1359525180291:dw|

4. anonymous

3 dot mean continued

5. anonymous

by the way 1/secx is cos right?

6. anonymous

ok sorry about delay...heres what your steps should be $x = 2\sin \theta$ $dx = 2\cos \theta d \theta$ $\rightarrow \int\limits_{}^{} \frac{2 \cos \theta}{4 \sin^{2} \theta} (2 \cos \theta) d \theta$ $= \int\limits_{}^{}\frac{ \cos^{2} \theta}{\sin^{2} \theta} d \theta$ $=\int\limits_{}^{}\frac{1-\sin^{2} \theta}{\sin^{2} \theta} d \theta$ $=\int\limits_{}^{} \csc^{2} \theta - 1$ $= \cot \theta - \theta +C$

7. anonymous

it should be -cot0 -0 + c

8. anonymous

i believe

9. anonymous

ahh right sorry

10. anonymous

and yep i did the same steps as you ty a lot for your help

11. anonymous

yw

12. anonymous

and thanks a lot for taking time to clear my confusions

13. anonymous

and you did in so many fewer steps then me going have to start doing it in my head as well

14. anonymous

can i message you later if i have more questions in my homework :)

15. anonymous

sure thing ... and i did skip some steps just for sake of time and space, but on paper its good to be thorough so you don't make any mistakes

16. anonymous

ok ty