anonymous
  • anonymous
I'm confused with this question...
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
anonymous
  • anonymous
I keep getting the last 2 parts wrong >.<
anonymous
  • anonymous
For #3 shouldn't it just be base times height divided by 2?

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ganeshie8
  • ganeshie8
|dw:1437018844512:dw|
ganeshie8
  • ganeshie8
Keep in mind, the definite integral gives the "signed" area between x axis and curve
anonymous
  • anonymous
Right so it's (2x2)/2 isn't it?
anonymous
  • anonymous
@ganeshie8 what does that mean?
ganeshie8
  • ganeshie8
that just means, definite integral gives the "negative" of the area below x axis and "positive" of the area above x axis
anonymous
  • anonymous
Ohhh right, so in that case isn't it only -2?
anonymous
  • anonymous
Ahh yep, that was my mistake!!
ganeshie8
  • ganeshie8
|dw:1437019097211:dw|
anonymous
  • anonymous
Haha right on!! :D that's correct... now what about the last one?
Astrophysics
  • Astrophysics
oOoOoOo
ganeshie8
  • ganeshie8
Just to be clear : Area is never negative. But the definite integral doesn't give you the actual area, it gives you the "signed" area. A negative sign is added to the area below x axis and a positive sign to the area above x axis
anonymous
  • anonymous
Ahaha XD lol @Astrophysics
anonymous
  • anonymous
Mhmm that makes sense!
ganeshie8
  • ganeshie8
Find the blue area and add up everything |dw:1437019419001:dw|
anonymous
  • anonymous
But that shape's neither a rectangle nor a triangle...
ganeshie8
  • ganeshie8
try again, its not hard for you im sure
Astrophysics
  • Astrophysics
Easy way, err Hint: |dw:1437019699663:dw|
anonymous
  • anonymous
|dw:1437019750270:dw| or like this?
ganeshie8
  • ganeshie8
looks good, keep going and finish it off
Astrophysics
  • Astrophysics
Yeah, exactly :D
anonymous
  • anonymous
So that small triangle's area would be 2(-1) / 2 = -1 and then the rectangle above it... 2(-1) = -2 so then would it be -1 - 2 = -3 ?
anonymous
  • anonymous
I feel like I'm doing it wrong :/
anonymous
  • anonymous
Yep its wrong
ganeshie8
  • ganeshie8
Keep in mind : Length, area and volume can never be negative by the very definition
ganeshie8
  • ganeshie8
|dw:1437020002007:dw|
anonymous
  • anonymous
Ohhh so no negative sign in the calculations but at the end we just say its negative since its below the x-axis?
ganeshie8
  • ganeshie8
Yes, the area in its usual interpretation is always positive. To work the definite integral between 0 and 9, simply add up the areas above x axis and subtract the areas below x axis
ganeshie8
  • ganeshie8
|dw:1437020162395:dw|
anonymous
  • anonymous
I got 1! and it's CoRrEcT :DDD Thanks so much @ganeshie8 & @Astrophysics!! You guys are the best! :D
Astrophysics
  • Astrophysics
Lol I didn't do much, it's all ganeshie and his amazing explanations xD
anonymous
  • anonymous
@Astrophysics you both did a lot! :D It all helped :D
anonymous
  • anonymous
Thanks again!
ganeshie8
  • ganeshie8
np :) in light of above problem, just want to give you this result : If \(f(x)\) is odd function, then \[\int\limits_{-a}^a f(x)\, dx = 0\] try figuring out why that must be true when you're free and if you want to :)
anonymous
  • anonymous
Yeah my prof was saying something about even and odd functions too... like because even functions are symmetric or something like that...? xD lol
ganeshie8
  • ganeshie8
Yes it has to do with symmetry about origin (0, 0). It would be more fun if you figure it out on ur own because you're not very far from seeing it on ur own. Good luck!
anonymous
  • anonymous
Yuppers! Haha thanks! :D
Astrophysics
  • Astrophysics
Yeah, that's a fun one, you can try the trig functions and see as well
Astrophysics
  • Astrophysics
Also for even then \[\int\limits_{-a}^{a} f(x) dx = 2 \int\limits_{0}^{a} f(x) dx\] try working this out to
anonymous
  • anonymous
Oooh you guy know so much about calculus *_* hahaha thats awesome! Will definitely look at those :D
anonymous
  • anonymous
guys* xD haha
Astrophysics
  • Astrophysics
Lol, well I don't know about ganeshie (he's probably mastered it) but I'm still learning...especially vector calculus that course was weird xD, I still don't fully understand it.
anonymous
  • anonymous
Oh myyy... if you don't understand it i wonder how terrible that course would go for me XD Lol
Astrophysics
  • Astrophysics
No, I think you will be fine, I just had a later start at math, I didn't "really learn" math till I was around 18...and I'm not too far from that right now haha. So I guess I struggle a bit more in understanding the concepts but I guess it's not too bad, I've learnt quite a few things past 2 years :P
anonymous
  • anonymous
Haha thats pretty awesome!! xD Well, all I know that this is gonna be the last math course I'll be taking for a while XD hahaha
Astrophysics
  • Astrophysics
Hehe, I used to hate math and say the same thing, now I just want to keep learning it :P
anonymous
  • anonymous
LOL it was the exact opposite for me!! I graduated from high school with a Pre-Calculus score of 99% (and i LOVED math) .... I'm not gonna tell you my grades now :P hahaha
Astrophysics
  • Astrophysics
Haha, well I'm not going to tell you what to do, I think you will figure out doing what you enjoy xD, anyways have fun learning calculus, integrals are pretty awesome, but frustrating at times but that's the fun part! So enjoy!
anonymous
  • anonymous
Thanks!! :D You're super kind... and smart =D
Astrophysics
  • Astrophysics
Haha, thanks and right back at ya :D
anonymous
  • anonymous
Haha merci beaucoup ;D

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