Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [bounds-of-integration]

In many questions the problem of determining bounds of integration in multiple integrals is a major part of what an answer needs to deal with, and in surprisingly many questions it is the only issue. This tag is for such occasions.

Common topics include:

  • Switching the order of iterated integrals to find new bounds
  • Determining the bounds of a region after performing a change of variables
  • Classifying regions of different dimensions when applying one of Green's, Stokes's, or Divergence Theorems
  • Recovering the limits of integration from the passage of a Riemann sum to a definite integral
114 questions
5
votes
3 answers

Is it correct to write $\int_a^x f(x) dx$?

The question pretty much sums it all. A few days ago when studying how to find the real part of a function knowing the imaginary part (or vice versa) I was given this formula: $$u(x, y) =\int_{x_0}^{x} \frac{\partial u} {\partial x} (x, y_0) \,dx +…
user556151
1
vote
1 answer

Problem while using divergence theorem

Evaluate $$\iint_S \mathbf A\cdot n \ \mathrm d S$$ where $\mathbf A=y\mathbf i+2x\mathbf j-z\mathbf k$ and $S$ is the surface of the plane $2x+y=6$ in the first octant cut off by the plane $z=4$ I was doing this problem then $\operatorname{div} A =…
user187604
  • 409
0
votes
1 answer

Finding the bounds of integration for a vector valued function

I am trying to find the arc length of $r(t) = (\sqrt{2}t)i + (\sqrt{2}t)j + (1-t^{2})k$ from $(0, 0, 1)$ to $(\sqrt{2}, \sqrt{2}, 0)$. I know how to find the integral except I am not sure what the bounds of integration should be. I know $t$ can't…
dumbitdownjr
  • 97