Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007

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[adedsfsdedasewdaww]

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[agapitoflores001]

I feel embarrassed that I am a slow learner. I have to watch this again.

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[kotofu]

the lectures are getting more and more exciting. Differential was rather boring.

[datHulkinZ]

(x-a)^2+y^2=a^2 i don't get it it looks like pitagor theorem but where did it match

[chrisgeorge9]

@datHulkinZ

thats the equation of a circle whose origin is at (a,0) and radius a

[adedsfsdedasewdaww]

@datHulkinZ its the general frmula for a circle O-O

[gorgolyt]

witch plural is witches! :0

[TWICEfan3125]

@gorgolyt he's a Math professor, not an English professor!

[gorgolyt]

@TWICEfan3125 and i'm a maths undergraduate :V

tbh mathematicians tend to be particularly concerned about grammar, all of my lecturers are impeccable.

and this guy was so irked by his mistake it actually turns out he addressed it in the next lecture!

[ryecheese999]

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[KatherineRogers]

Take the integral from 0meters to (a meters) if along the y axis and from 0 meters to the (square root of a meters) if along the x direction i.e. use UNITS. This helps ensure the units of the answer come out properly. Again, dont delete k in y=kx^2 because its numerically equal to one, the units are needed. k=1/(1 meter). k is exact so does not effect significant figures of your answer.

[mafl25]

@KatherineRogers First: When he says that y=x^2, he's talking about the Magnitude of x squared, not the unit squared. Here is an example: Imagine I have a sheet of paper whose width is 10 cm and its length is the width squared. The length will then be 100 cm, NOT 100 cm^2 right? This is because only the magnitude (the number itself) was squared, not the unit. The same thing happens with the problem he's solving.

[mafl25]

@KatherineRogers Second: If we take “a” as the height of the figure, then the equation would be V= (pi/2)h*a, (remember that height is NOT unit squared). We could also write “a” as “x”(or radius) squared, so the final equation would be V=(pi/2)h*r^2 which won’t have any problem with units. I hope I made myself clear.

[TomasPetricek]

@KatherineRogers Actually, if a constant k=1/1m is used, then in the final formula for V you will end up with subtracting m^1 from m^2 which is apparently not correct.

[KatherineRogers]

Y=x^2 NO!. Meters does not equal meters squared. Try Y=kx^2 where k is a unit conversion factor ie 1/(1meter).In cm, the k would be 1/(100cm) Make SURE your equation is dimensionally correct BEFORE you work with it. The constant k also appears in the answer making volume be in meters cubed (or cm cubed) as volume should be. This lecture was a mess and should be redone!

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[jmwilcoxon]

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