Question

What does the dx mean in \[ \int e^x\cdot dx \] ?

Answer 1

does it denote the infinitesimal?

Answer 2

it means that the variable for integration is x
in \(\int ye^x dy\)
the variable for integration will be y and the answer will be e^x * y^2/2

Answer 3

yes, and the interpretation of the entire integration will be that your are adding very small(infinitesimally small) intervals of 'x' of the curve e^x

Answer 4

so i would say yes, dx denotes infinitesimal small intervals of x

Answer 5

cool, hence, when integrating by substituting with "u", du denotes infinitesimally small intervals of "u" ... please have a quick look at my geogebra screenshot and tell me if you can help with the question I ask therein

Answer 6

that is just co-incidence, the curve is f(x)= x^2, so f(3)=9
and area is also 9 by integration as \[\int\limits_{0}^{3}x^2dx=9\]
u don't get the functional value at boundary every time you integrate.
here integration gives you area

Answer 7

yes, but i've noticed it comes up often enough to be statistically significant, if not to be predicted by theorem

Answer 8

I think it's inevitable for any polynomial. Don't think there's any special significance to it. Not sure on that however.

Answer 9

u get it only when the lower limit is 0 and f(0)= 0
\([f(x)]^a_b=f(a)-f(b)=f(a) \quad\text{if b=0 and f(0)=0 }\)

Answer 10

i'll test it Algebraic! meantime, hartnn, here is another

Answer 11

hartnn: And does this apply in every instance where these conditions obtain?

Answer 12

I don't think that's quite true @hartnn :)
http://www.wolframalpha.com/input/?i=plot+x%5E2+-2%2C++x%5E3%2F3+-2x&dataset=&asynchronous=false&equal=Submit

Answer 13

in this case u don't get it exact as 625 because u took it fron 1 to 5
if u would have taken from 0 to 5, u get 625

Answer 14

okay, here is one fer y'awl to cogitate upon