Question

I felt like making up an integral for people to try to solve for fun. Good luck!

Answer 1

OH NO! I had a typo in my question, the 9 in the numerator was supposed to be a 4! \[\int\limits_{-9}^{9}\frac{ (36-4x^2)^{3/2} }{ 9-x^2 }dx\]

Answer 2

oh :c

Answer 3

Sorry Zepdrix. Hopefully that makes it easier. >_> I'm so sorry, I checked it like 10 times and typed the wrong thing ugh lol.

Answer 4

That makes it quite it bit easier to work through c: heh

Answer 5

I'm just experimenting with creating problems, since I'm usually just solving them. If you're interested in making some or if you've seen some particularly fun/interesting/tricky ones please feel free to share lol.

Answer 6

Well, promise this is the last correction, the limits of integration are -3 to 3, I think I'm tired from too many finals and studying all week... I swear it's an entirely legitimate problem this time.

Answer 7

Mmmmmmmmmmmmm I came up with 96ish.. am i close am i close??? O:

Answer 8

I might as well write out the steps and go to sleep, but you are rather close. I'm curious what you did, the answer should contain pi in it.

Answer 9

Hmmm.
I did a trig sub, x=3sinQ, dx=3cosQ dQ.

There were quite a few steps :) It's possible I goofed up somewhere heh

Answer 10

\[4\int\limits_{-3}^{3}\frac{ (4(9-x^2))^{3/2} }{ 4(9-x^2) }dx\]\[4\int\limits_{-3}^{3}\sqrt{4(9-x^2)}dx\]\[8\int\limits_{-3}^{3}\sqrt{9-x^2}dx\]From here you can see that this is a semicircle with radius of 3, so the integral becomes\[8*\frac{ \pi 3^2 }{ 2 }=36\pi \approx 113.0973355\]

Answer 11

Oh neato :o

Answer 12

Haha I'm scared to imagine what trig substitution would bring! I almost want to try it and find out, but yeah I saw an integral like this today and was pretty shocked and looks awesome lol. =D

Answer 13

subbing function:
\[\large \sin\theta = \frac{1}{3}\sqrt{9-x^2}\]
\[\large 3 \sin \theta = \sqrt{9-x^2}\]

subbing derivative:
\[\large \cos\theta=\frac{1}{3}x\]
\[\large x =3\cos\theta\]
\[dx=-3\sin\theta \space d\theta\]