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How do I solve the following integral?$$I = int_0^{pi} e^{-frac{1}{2}cos x} cos left( 3x + frac{1}{2} sin x right) dx$$ I suppose this can be solved...
Asked on 12/25/2021 by Denis Korzhenkov
1 answerIs there any way to get the equation of axis of reflection given two intersecting lines without sketching?Example question: The image of the line $p:; y-2x=3$ is the line...
Asked on 12/25/2021 by Ham Tesh
3 answerLet $A$ be a finite abelian group. I have read that there is an isomorphism of abelian groups between the group $H^2(A;mathbb{C}^{times})$, and the group of skew-symmetric bicharacters...
Asked on 12/25/2021
0 answerThis is a self-answered question. I post it here since (embarrassingly) it took me some time to realize that the solution is obvious. Let $D subseteq mathbb R^2$ be...
Asked on 12/25/2021
1 answerJust as we define the signed curvature of a plane curve as the rate of change of the angle through which a constant vector must be rotated to bring it...
Asked on 12/25/2021 by user452965
0 answerI have following question. I hope to solve the inequality: $frac{x^2}2 - x + frac{x}{ln(x) -1} < frac{x^2}2$ in what conditions will be OK? ie, which values for...
Asked on 12/23/2021 by sunnytestdata
1 answerLet $T:Vrightarrow V$ be the linear transformation defined as follows: If $fin V, g=T(f)$means that $$g(x)=int_{-pi}^{pi}{1+cos(x-t)}f(t)~dt$$Find all real $c neq 0$ and all nonzero ...
Asked on 12/23/2021
1 answerIn the following question-Let a, b, c be positive real numbers. Prove that $$sum_{cyc} {a^3over a^3+b^3+abc} ge 1.$$In here, there is no constraint given.But in the solution, the...
Asked on 12/23/2021
2 answerSuppose A $xrightarrow{f}$ B $xrightarrow{g}$ C is exact in an abelian category. f and g has factorization f = me and g = m'e' where m and m'...
Asked on 12/23/2021 by gerrard
0 answerI was analyzing my data in Origin and I did the numerical differentation. I wanted to find the maximum of $frac {dM}{dT}$. The black curve corresponds to $frac...
Asked on 12/23/2021
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