# stopandthink

Senior Members

35

1. ## Area under a curve

Yes, it's just a simple straight line. Also, thank you for helping me out
2. ## Area under a curve

Great! so now I understand how to find the definite integral of two positive points on the x axis. And also that I must add a constant to an Indefinite Integral. Although, I'll admit that I'm confused now with finding the definite integral of positive negative limits. Basically I just split it into parts, get the absolute value, and then add both parts, I think? --------------------- hold on so if someone asked for the definite integral of your example would you give them 0 or 16 as the answer? I see that area is not the same as definite integral. Hmmm

Don't know but cool idea . Hope someone helps you out
4. ## Area under a curve

$\int_{0}^{4}x^2 dx=?$ is this how you start it off? No ones asking me, I'm simply trying to learn how to integrate on my own. I just chose those points for simplicity Okay I think I figured it out.. So first i take the integral of my function $x^2$ which is $1/3x^3$ then I plug in 4 for x and get 21.3 then I plug in 1 for x and get 0.3 then I subtracted 21.3 - .3 = 21 sweet!
5. ## Area under a curve

$f(x)=x^2$ How do I go about finding the area under x=[0,1,2,3,4]?? I'm a beginner at definite Integrals so please make an easy explanation. Thanks!

Grapefruit
8. ## flouride

So we can die with a full set of teeth?
9. ## really confused and new

My mass- 72kg speed of light- 186000 miles/sec $E=72(1.86*10^5)^2$ correct? So we all have a great amount of potential energy, but since i'm made of stable atoms then its almost impossible to ever use that energy? correct?
10. ## Distance in space

So basically what i thought up of last night has data to support it. I'll look into J. Richard Gott's calculations.
11. ## Distance in space

I'm not a specialist in cosmology so i won't be surprised if most of this is incorrect. Everything we can see, in the universe, travels from point A to B, in waves. So i know when i look at the sun, I'm seeing it how it was 8 minutes ago. But when we look through a powerful telescope we can see nebula's and galaxies further away from us in space, whose waves are just arriving from a long trip through space. And just like the sun we can observe them how they once looked. But since space is expanding we must also take into consideration that the light took longer because new space was forming as it traveled. Making it cover more distance but also having more distance to cover ahead towards it's destination. I'm not sure how much new space is formed per light year, but i presume it's not much. Anyway taking all this into consideration i can now assume that what i'm looking at are photons ,from galaxies in the past, that were once way closer, but in reality they are actually further away in space. My question is how do cosmologist, physicist, etc.. calculate a "finite" observable universe when space is probably bigger than what we think it is? If it's measured by observation then all were doing is measuring the past.
12. ## Experiment: A Party Trick that Sucks.... Liquid!

She corrected herself in the info under the video. "CORRECTION: The pressure inside the glass increases as the fire heats up the molecules. Oxygen is being "consumed" by the fire, that produces Carbon Dioxide (the matter itself remains, no matter is mysteriously 'vanishing' or 'created' out of nothing!). But now, the pressures are different and therefore the water outside the glass are pushed inwards — the lower pressure of the INSIDE 'sucks in' the liquid around it under the pressure stabilizes."
13. ## Derivative

Ok, i think i understand better now what the derivative is. By drawing out a graph $f(x)=x^2$ with x=time(in seconds), y=velocity(mph) So when $\frac{2seconds} {4mph}$, $\frac{3seconds} {9mph}$ So the difference is 5mph, but as you get closer and closer to exactly 3 seconds you find that it's instantaneous velocity(derivative) is 6mph...?

15. ## Derivative

Ok so i just learned that f'(4)=8 is the point on a new graph f'(x) that overlaps the original graph f(x), which is why i couldn't understand where it belonged...
16. ## Derivative

I'm not expecting a different answer because i know how to find the "derivative", Of this simple function. Ok, so i think of a derivative as rise/run=slope... and i can find the slope of a secant line easily but what we want to do is get the secant line as close to the tangent line. So when we do arrive at the tangent line, we find that it's 8.... but i have no clue as to what i'm looking at on a graph with this number..
17. ## Derivative

I know that it's when a secant line gets closer and closer to the tangent line at the co-ordinates (4, 16) ... so when we get really close we get 8 as a "derivative"... but i still know nothing about a derivative.
18. ## Derivative

$f(x)= x^2$ $f(4)=16$ $f'(4)=8$ What exactly is the derivative giving me?
19. ## ACT test

Thank you, I was hoping i could use it. I still need a good score to get into a decent college tho.
20. ## ACT test

Speaking of calculators, do you know if the TI-84 is allowed?
21. ## ACT test

I take the ACT test on the 27th of this month. And I'm sure it's not as difficult as I think it is, but i could be wrong. I'm really stressing about it because I plan on applying for FAFSA, and of course a higher score means a better chance of getting financial help. Any advice? any at all..
22. ## Differentiating

Could you explain how to use the foil method on this? ------------------------------------------------------------------------- I'm just going to review the binomial theorem.
23. ## Differentiating

Like this? $x^2+dx(x)+dx(x)+dx^2(x+dx)$ ---I have absolutely no clue as to what to do next
24. ## Differentiating

$y= x^3$ $y+dy= (x+dx)^3$ My question is how would i go about cubing x+dx? I can use the foil method easily with squaring, but i can't quite see how on this.
25. ## 2 @ 2 = 4

I don't really see what's so fascinating, but maybe it's just me.
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