MHB Improper Integral and Force on a Dam

ineedhelpnow
Messages
649
Reaction score
0
my final is tomorrow and my instructor gave a list of questions that will be similar to the ones on the final exam and i want to see how they should be done properly. I've been working on other problems but i can't get past these ones. thanks

$\int_{-\infty}^{0} \ \frac{dx}{(2+x) \sqrt{x}}$

a graph of $y=\frac{x^2}{4}$ is given with intersection point $(4,4)$. find the total force of the dam using coordinate system at the bottom of the dam. (i don't even know what this question means)
 
Last edited:
Physics news on Phys.org
there's an example here that's similar to the second question but it doesn't really make sense?? it's on the last page.

View attachment 2876
 

Attachments

I'm not at the level of math that you are on, but I can help you on the first improper integral. If you make the substitution $$x = u^2$$, the integral will simplify into a form that you can easily take its anti-derivative. Then you can proceed as you would normally with a normal improper integral, taking into consideration that it has a discontinuity at x = -2, and x = 0.
 
appreciate the help Rido :)for that one i thought i needed to integrate it t to 0 and then take the limit as t goes to -$\infty$ i realized my mistake because i hadn't noticed that's undefined at -2 (thank you for pointing that out) so i guess i have to integrate from -$\infty$ to -2. and then from -2 to 0.
 
You might find this thread helpful for the question regarding hydrostatic forces:

http://mathhelpboards.com/questions-other-sites-52/ns-questions-yahoo-answers-regarding-hydrostatic-forces-6150.html
 
ineedhelpnow said:
$\int_{-\infty}^{0} \ \frac{dx}{(2+x) \sqrt{x}}$
I'm not quite sure why no one has made this comment...The integrand does not exist for negative x because of the square root. There is no integration to do here. Or am I missing something obvious?

-Dan
 
I noticed that too, because if you tried to integrate, you'd have to sub in negative infinity into arctan(sqrt(x/2)), but I didn't want to comment because I wasn't sure.
 
when i was integrating it i got some weird answers but i tried to ignore it and kept going on. :D
 
for the interval on the dam (in the example), the bottom of the dam was at the point 0 on the y-axis but why did the interval go upto 25?
 
Back
Top