## sat_chen 2 years ago verify my trigonometric substitution

1. sat_chen

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

2. sat_chen

|dw:1359525159259:dw|

3. sat_chen

|dw:1359525180291:dw|

4. sat_chen

3 dot mean continued

5. sat_chen

by the way 1/secx is cos right?

6. dumbcow

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. sat_chen

it should be -cot0 -0 + c

8. sat_chen

i believe

9. dumbcow

ahh right sorry

10. sat_chen

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

11. dumbcow

yw

12. sat_chen

and thanks a lot for taking time to clear my confusions

13. sat_chen

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

14. sat_chen

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

15. dumbcow

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. sat_chen

ok ty