Jan 17, 2010 · Also related, by convention, the bounds of the integral determine the sign. In other words, the integral of f from a to b is the OPPOSITE of the integral of f from b to a. In the Riemann sums, basically, the dx's can be negative, too. It doesn't make a lot of sense from a geometric standpoint, but algebraically, it makes a lot of sense.

Jul 14, 2014 · If you read it correctly you will see that it says 'the "area" may be negative but area is always positive'. The first "area" is in quotes which means that it is using the word in a very loose sense. It is saying that the integral you get, which if it were above the x-axis would be the area, is negative so cannot be the actual area.

Mar 29, 2020 · The integral knows because lower and upper makes the difference. The underlying sign comes from the orientation of the ##x-##axis. So the coordinate has a direction and the integral respects orientation, or better: differential forms respect orientation. That is why volume ##dx\wedge dy \wedge dz## has an orientation, too.

Sep 21, 2004 · Hi guys, I am looking in my calculus book, and it tells me in the example problem that the Integral of e^(-x)dx = -e^(-x) I don't see how u get this answer. I know the integral of e^x = e^x but how does that negative sign come out to the …

Aug 17, 2023 · Homework Statement If the voltage between two points is the negative integral from A to B of Edl, then in a given problem where it asks me to find the voltage between two points, how do I know which is A and which is B?

Apr 11, 2023 · No. The left-most integral above has the limits of integration in the wrong order, so the value of the integral will be negative, as you found. If you rewrite the limits in the proper order -- left to right or bottom to top, then you'll get a positive value. Your integral should have its limits like so: ##\int_{-1}^3 x^2 \, dx##.

Integral Negative Feb 7, 2012 #1 bmed90. 99 0. If you integrate 1/(1-y)dy why do you end up with a ...

Aug 9, 2014 · Yes, you can use other methods. The most common of these is to integrate the constant function 1 over the 3-dimensional region (or the integral of the characteristic function of the region). Typically this is done with an iterated triple integral:$\displaystyle V = \int_a^b \int_{f_1(x)}^{f_2(x)}\int_{g_1(x,y)}^{g_2(x,y)}\ dz\ dy\ dx$

Oct 9, 2009 · The question came from the fact that in electromagnetism, we define the potential by the negative of the integral with swapped limits. I'm not sure why you would put the extra step in there if there wasn't a case where the positive with the limits restored wouldn't be equivalent.

May 12, 2012 · Compute the surface integral for F = [3x^2, y^22, 0] and S being a portion of the plane r(u,v)=[u,v,2u+3v], 0≤u≤2, −1≤v≤1. The Attempt at a Solution I managed to get the correct answer, because with some luck I defined the normal in the correct direction. I am just confused on when this answer is negative or positive?