- anonymous

I'm confused with this question...

- jamiebookeater

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- anonymous

##### 1 Attachment

- anonymous

I keep getting the last 2 parts wrong >.<

- anonymous

For #3 shouldn't it just be base times height divided by 2?

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## More answers

- ganeshie8

|dw:1437018844512:dw|

- ganeshie8

Keep in mind, the definite integral gives the "signed" area between x axis and curve

- anonymous

Right so it's (2x2)/2 isn't it?

- anonymous

@ganeshie8 what does that mean?

- ganeshie8

that just means, definite integral gives the "negative" of the area below x axis and "positive" of the area above x axis

- anonymous

Ohhh right, so in that case isn't it only -2?

- anonymous

Ahh yep, that was my mistake!!

- ganeshie8

|dw:1437019097211:dw|

- anonymous

Haha right on!! :D that's correct... now what about the last one?

- Astrophysics

oOoOoOo

- 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

Ahaha XD lol @Astrophysics

- anonymous

Mhmm that makes sense!

- ganeshie8

Find the blue area and add up everything
|dw:1437019419001:dw|

- anonymous

But that shape's neither a rectangle nor a triangle...

- ganeshie8

try again, its not hard for you im sure

- Astrophysics

Easy way, err Hint: |dw:1437019699663:dw|

- anonymous

|dw:1437019750270:dw|
or like this?

- ganeshie8

looks good, keep going and finish it off

- Astrophysics

Yeah, exactly :D

- 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

I feel like I'm doing it wrong :/

- anonymous

Yep its wrong

- ganeshie8

Keep in mind : Length, area and volume can never be negative by the very definition

- ganeshie8

|dw:1437020002007:dw|

- 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

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

|dw:1437020162395:dw|

- anonymous

I got 1! and it's CoRrEcT :DDD Thanks so much @ganeshie8 & @Astrophysics!! You guys are the best! :D

- Astrophysics

Lol I didn't do much, it's all ganeshie and his amazing explanations xD

- anonymous

@Astrophysics you both did a lot! :D It all helped :D

- anonymous

Thanks again!

- 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

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

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

Yuppers! Haha thanks! :D

- Astrophysics

Yeah, that's a fun one, you can try the trig functions and see as well

- 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

Oooh you guy know so much about calculus *_* hahaha thats awesome! Will definitely look at those :D

- anonymous

guys* xD haha

- 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

Oh myyy... if you don't understand it i wonder how terrible that course would go for me XD Lol

- 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

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

Hehe, I used to hate math and say the same thing, now I just want to keep learning it :P

- 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

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

Thanks!! :D You're super kind... and smart =D

- Astrophysics

Haha, thanks and right back at ya :D

- anonymous

Haha merci beaucoup ;D

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