So I have a math project and basically (I didn't mean to) I ended up with these really complicated integrals that i have no idea how to solve. any help would be amazing!! Or if you just have a wolfram alpha pro account that would be incredibly helpful as well😊
$$\frac{dx_L}{dt} = \frac{-112}{\sqrt{2t^2-38t+221}}$$ and
$$\frac{dx_L}{dt} =\frac{8t}{\sqrt{2t^2-38t+221}}.$$
#Help with my integrals
celest apex
warm loomBOT
So I have a math project and basically (I didn't mean to) I ended up with these ...
- Do not ping the Moderators, unless someone is breaking the rules.
- Do not ping the Helper Moderators, unless there is a conflict between helpers.
- Do not ping other members randomly for help.
- Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
- Wait patiently for a helper to come along.
- If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:
+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:
void gateBOT
brook
celest apex
if it wasn't clear im finding the integral of each equation above
tender pecan
if it wasn't clear im finding the integral of each equation above
You can *modify the denominator like this :
2tt -38t +221
2(tt-19t) +221
2(t-19/2)^2 +221 -2(19/2)^2
I believe this strategy is called completing the square, from quadratic stuff, you can look it up
In the end, upon simplification, you will have something of the form
a(x-b)^2+c
in the square root in the denominator
That should put the integral in a standard form
rapid bloom
if it wasn't clear im finding the integral of each equation above
for the first one just complete the square, for the second you can let u=2t^2-38t+221, thus du=(4t-38)dt and 2du=(8t-76)dt
celest apex
ok thank you guys! if I complete the square, do i then need to use a trig sub?
rapid bloom
?tag helping
uneven galeBOT
**When helping people, please do not dump the full solution. **
Remember that these people are trying to learn concepts, and our goal should be to reinforce them. Giving them a solution will not help.
**Instead, give them hints and guide them toward the correct solution. **
You can ask things like "what part did you get stuck on?" or "what have you tried so far?" or give them a small starting hint. This ensures better learning. For more tips, reach out to Schlaumau (@schlaumau).
rapid bloom
ok thank you guys! if I complete the square, do i then need to use a trig sub?
yes, but it should be known by now that $\int\frac{1}{\sqrt{a^2-x^2}}=\arcsin(\frac{x}{a})+C$
void gateBOT
temu mod | promote to mod pls
agile lakeBOT
@celest apex