## gvm 3 years ago does the integral x/(5-x)^(1/2) dx that goes from 1 to 5 converge and if so what is the value and how do you find it?

1. princeofwetlot

$\Large \int_1^5 \frac{x}{\sqrt{5-x}}dx?$

2. gvm

yes that's what it looks like...so does it converge? and how do you show that it converges?

3. princeofwetlot

well you do this: $\Large \lim_{t \rightarrow 5} \int_1^t \frac{x}{\sqrt{5-x}}dx$

4. gvm

yup i have that so far :)

5. princeofwetlot

i am thinking trigonometric substitution for this...

6. princeofwetlot

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7. princeofwetlot

$\large \sqrt 5 \sin \theta = \sqrt x$ $\large \sqrt 5 \cos \theta = \sqrt{5-x}$ $\large 5 \sin^2 \theta = x$ $\large 10 \sin \theta \cos \theta d\theta = dx$ $\large \int \frac{x}{\sqrt{5-x}}dx = \int \frac{5\sin^2 \theta \times 10 \sin \theta \cos \theta d\theta}{\sqrt 5 \cos \theta}$ $\large \frac{50}{\sqrt 5} \int \sin^3 \theta d\theta$ i believe that is solveable?

8. princeofwetlot

do you still need help?

9. gvm

i think i'm all set now...thank you :) i just have to ace this take home test because if i get a one hundred on it i'll get exempt from the final :D

10. gvm

thank yoouuuu! :)

11. princeofwetlot

no probs ^_^ keep practicing to see these things easier hehe

12. gvm

are you in college or high schoool?

13. princeofwetlot

college

14. gvm

neato :) where do you go?

15. princeofwetlot

probably a university you dont know lol

16. gvm

oh alright then...just curious cuz i'm starting colllege in the fall! weeee :D

17. princeofwetlot

congrats :D

18. gvm

thank you :) ughhh its sooo early where i live...i pulled an all nighter :O