Integral: Right Approach? Checked with Derivative?

[rocomath]

anyone have time to waste? lol, I've been trying to check it with the derivative but either I'm messing up or it's wrong, but i just feel like i did it right ... I'm just having a hard time computing

also, did i take the right approach? thanks.

 

[Dick]

It's not really clear what integral you are actually trying to solve. Is there really a t^2 in the exponent? Is the sinh multiplying that?

 

[rocomath]

It's not really clear what integral you are actually trying to solve. Is there really a t^2 in the exponent? Is the sinh multiplying that?

sorry, the parenthesis is meant for a substitution

$$\int e^{-t^2}dt$$

 

[Dick]

You can't find an indefinite integral of e^(-t^2) in terms of elementary functions. The indefinite integral is called 'erf' (modulo constants).

 

[rocomath]

damn.

 

[dynamicsolo]

I've got a separate question about this: is that upper limit really 'ln 1'? Wouldn't that make the two limits of integration identical? Is someone pulling your leg on this one? Is it a trick question?

 

[rocomath]

I've got a separate question about this: is that upper limit really 'ln 1'? Wouldn't that make the two limits of integration identical? Is someone pulling your leg on this one? Is it a trick question?

it's from the MIT OCW website

http://ocw.mit.edu/NR/rdonlyres/6055BD0B-FEA6-4BBD-AB05-9E9D81615CAA/0/ocw01exam3.pdf

lol it is both 0, i didn't even notice.

 

[dynamicsolo]

it's from the MIT OCW website

http://ocw.mit.edu/NR/rdonlyres/6055BD0B-FEA6-4BBD-AB05-9E9D81615CAA/0/ocw01exam3.pdf

lol it is both 0, i didn't even notice.

Bwah-hah-hah! As a classical MIT nerd would declare, "You've been hacked!" (That does explain why that question's only worth 3 points. The lecturer was probably checking to see who was awake...)

Whoa! Good ol' 18.01 -- takes me back...

ProTip: Watch out if someone at MIT has something to do with an exam like this. They love to pull a fast one on the unwary at some point... (It's a place where parties unknown break into a "secure" area and adorn the Great Dome of the main building with something monumental almost every year.* They also measure bridge spans in smoots... What can you expect?)

*In 2003, to mark the centennial of heavier-than-air aviation, a rough reproduction of a Wright Flyer appeared atop the building overnight...

 

[Gib Z]

Thats an MIT test? I don't believe you. Here I was thinking MIT was an elite University...what grade is test meant to be for?

 

[HallsofIvy]

Thats an MIT test? I don't believe you. Here I was thinking MIT was an elite University...what grade is test meant to be for?

"18.01" is (college) freshman calculus. Every freshman at M.I.T. either "places" in a higher math course or takes 18.01 first semester freshman year (that's my memory from way back). I wouldn't want to be "elitist" but if you look carefully at that test you will see many problems that are easy if you understand the concepts rather than just apply formulas.

 

[rocomath]

Bwah-hah-hah! As a classical MIT nerd would declare, "You've been hacked!" (That does explain why that question's only worth 3 points. The lecturer was probably checking to see who was awake...)

Whoa! Good ol' 18.01 -- takes me back...

ProTip: Watch out if someone at MIT has something to do with an exam like this. They love to pull a fast one on the unwary at some point... (It's a place where parties unknown break into a "secure" area and adorn the Great Dome of the main building with something monumental almost every year.* They also measure bridge spans in smoots... What can you expect?)

*In 2003, to mark the centennial of heavier-than-air aviation, a rough reproduction of a Wright Flyer appeared atop the building overnight...

um yeah, you're definitely a nerd, lol. surprisingly that i did notice that it was "worth" 3 points. but since i didn't notice the lower/upper limits, it didn't click.

 

[rocomath]

Thats an MIT test? I don't believe you. Here I was thinking MIT was an elite University...what grade is test meant to be for?

math http://ocw.mit.edu/OcwWeb/Mathematics/index.htm#undergrad

 

[dynamicsolo]

um yeah, you're definitely a nerd, lol.

Sorry, I wouldn't generally post something like that, but when I say that the "trick question" was from an MIT hour exam, it was hard to resist dropping into character.

I think that part of the point of these kinds of conceptual problems is to get students into the habit of looking for key ideas or peculiar details that may make a difficult-looking problem easy to solve -- certainly a valuable skill.

 

[rocomath]

ah I'm just teasin. i have a lot of respect for ppl's help. anyways, I'm glad i made that dumb mistake, i'll def. be more aware from now on. ;-]