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Tagged with bounds-of-integration upper-lower-bounds
9
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Prove/disprove upper bound and lower bound of the Integral
Hey I need to Prove or disprove this sentence:
$$
\frac{4}{9}(e-1) \leq \int_0^1 \frac{e^x}{(1+x)(2-x)} \, dx \leq \frac{1}{2}(e-1)
$$
using the infimum and supremum method for integrals, where m and ...
- 1
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Double integral: technique to derive the limitations of $y$ (or $x$)
$$\iint_Cy dxdy, \quad C=\{(x,y)\colon0\leqslant x\leqslant2+y-y^2\}.$$
It is simple to see $x=2+y-y^2$ is a parabola with the symmetry axes is $x$ and the vertex $(9/4,1/2)$. It is easy to find the ...
- 7,792
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Control $\int_0^\infty |\psi(x)|^2 dx$ by $\int_0^\infty \int_0^\infty K(x+y)\psi(x) \psi(y) dxdy$
Assume that $\psi(x)$ is bounded and integrable on $x \in [0,\infty)$ with $\int_0^\infty \psi(x) dx = 0$, and suppose that $K \colon (0,\infty) \to (0,\infty)$ is some kernel function satisfying $K(x)...
- 2,860
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Prove that $\int_0^1 e^{-tu}(1-u)^{\alpha}du\leq t^{-1}$ for $\alpha,t>0$
Let $\alpha>0$, I need to prove that there exists $t_0>0$ such that $$\int_0^1 e^{-tu}(1-u)^{\alpha}du\leq t^{-1}, \forall t>t_0.$$ I received help and found that by Watson's Lemma you could ...
- 13
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Determining Bounds of Theta for Double Integration of a Polar Region
Given the region $$ R:(x, y | x^2 + y^2 \le 4x) $$ And given the function $f(x, y) = \frac{x}{\sqrt{x^2+y^2}}$, find the double integral of the polar region.
So upon sketching the graph we get a ...
- 11
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Convolution of function... integral bounds?
Okay so for this question: Convolution of a function with itself
The answer stated that in the case of $x\le 0$:
the integral bounds are from 0 to x. Why is this?
I also don't understand why from $...
- 41
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2
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Lower bound $\int_0^\infty e^{-t-\frac{t^2}{2\sigma^2}}dt$ by $1-\frac{1}{\sigma^2}$
I am trying to show a lower bound $\int_0^\infty e^{-t-\frac{t^2}{2\sigma^2}}dt \geq 1-\frac{1}{\sigma^2}$. It seems like one could try integration by parts and get
$$
\int_0^\infty e^{-t-\frac{t^2}{2\...
- 97
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2
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Double Integral Bounds / Substitution
I am having trouble following these steps in a reading on multivariable calculus.
Due to a change of variables:
$ \displaystyle\int_0^1 \int_0^s v^7 dv \, ds = \...
- 27
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Multivariable Calculus - Change of Bound Help!
I am having trouble following these steps in a reading on multivariable calculus.
Due to a change of variables:
$ \displaystyle\int_t^T \int_t^s \theta_v dv \, ...
- 27