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ling
  • Member for 5 years
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13 votes

Integration of $\ln\sin x$ from 0 to$ \frac{\pi}{2}$by DUIS

4 votes
Accepted

How to calculate the derivative of $\int_0^x \left(\frac{1}{t}-[\frac{1}{t}]\right)dt$ at $x=0$?

4 votes
Accepted

$\int_ \frac\pi6^\frac\pi2 \frac {3dx}{2\sin2x+1}$

4 votes
Accepted

Calculate the determinant of $a_{ij} = \frac{(1+x)^{i+j-1}-1}{i+j-1}$

4 votes

Some easy inequality for a new day :)))

3 votes

$f \in C[-1,1]$, Prove ${\lim_{h \to 0^+}}{\int_{-1}^1 \frac{h}{h^2+x^2}f(x)\,dx} = \pi f(0)$

3 votes
Accepted

prove or disprove that:$a^2+b^2+c^2\leq \frac{27}{4}$

2 votes

Liouville Theorem for Harmonic Functions

2 votes
Accepted

Evaluate the triple integral $\iiint_E (x^2 +y^2 +z^2) dxdydz $ Where $E$ is a solid ellipsoid

2 votes

A Proof of sup(S + T) = sup(S) + sup(T).

2 votes
Accepted

How to use Holder inequality in PDE?

2 votes
Accepted

Real analysis proof regarding continuity and intermediate value theorem

2 votes
Accepted

Series Divergence - Apostol Calculus Vol I, Section 10.20 #10

1 vote

Prove the limit problem

1 vote
Accepted

Limit as radius approaches 0 of double integral bounded by unit circle

1 vote
Accepted

To Prove using the Integral Mean Value Theorem

1 vote

Definite integration evaluation of $\int_0^{\pi/2} \frac{\sin^2(x)}{(b^2\cos^2(x)+a^2 \sin^2(x))^2}~dx$.

1 vote

is $(1 + 1/\gamma)I - \dfrac{ee^T}{m}$ positive definte for any $\gamma > 0$?

1 vote
Accepted

Let $A$ and $B$ be two nilpotent matrices. Prove that $A+B$ is nilpotent

1 vote
Accepted

Convergence of $\sum_{t=0}^{\infty} t^{\alpha} \cos \omega t$

1 vote
Accepted

Minimum principle of superharmonic functions

1 vote
Accepted

Self-adjoint extension of closed symmetric operator

1 vote
Accepted

Find the length of AP such that $\theta$ maximum.

1 vote

Cauchy problem and right-saturated solution

1 vote

harmonic function is zero on complex plane

1 vote

To show $f=0$ a.e.

1 vote

Prove$\sum_{k=0}^{n} k \binom{n+1}{k+1} (\frac{1}{n})^{k+1} = 1$ by induction.

0 votes
Accepted

Prove Using L'Hopital's Rule And Mean Value Theorem.

0 votes
Accepted

How to calculate the inverse of Hessian matrix?

0 votes

Maximum and minimum of a fractional function