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AllQuestion and Answers: Page 1369

Question Number 67939 Answers: 1 Comments: 2

Question Number 67937 Answers: 0 Comments: 1

Question Number 67932 Answers: 1 Comments: 4

let A(θ) = ∫_0 ^∞ (dx/((x^2 +3)(x^4 −e^(iθ) ))) with 0<θ<(π/2) 1) calculate A(θ) interms of θ 2) determine also ∫_0 ^∞ (dx/((x^2 +3)(x^4 −e^(iθ) )^2 ))

$${let}\:{A}\left(\theta\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}^{\mathrm{4}} −{e}^{{i}\theta} \right)}\:\:{with}\:\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}\left(\theta\right)\:{interms}\:{of}\:\theta \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}^{\mathrm{4}} −{e}^{{i}\theta} \right)^{\mathrm{2}} } \\ $$

Question Number 67931 Answers: 0 Comments: 0

let A_n =∫_0 ^(π/4) x^n {1+cosx +cos(2x)}^2 dx find a relation of recurrence betwedn the A_n

$${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{x}^{{n}} \left\{\mathrm{1}+{cosx}\:+{cos}\left(\mathrm{2}{x}\right)\right\}^{\mathrm{2}} {dx} \\ $$$${find}\:{a}\:{relation}\:{of}\:{recurrence}\:{betwedn}\:{the}\:{A}_{{n}} \\ $$

Question Number 67927 Answers: 0 Comments: 9

Tinku Tara,the developer. Sir, I don′t receive notifications from the forum.Pl fix the problem.

$$\mathrm{Tinku}\:\mathrm{Tara},\mathrm{the}\:\mathrm{developer}. \\ $$$$\mathrm{Sir}, \\ $$$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{receive}\:\mathrm{notifications}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{forum}.\mathrm{Pl}\:\mathrm{fix}\:\mathrm{the}\:\mathrm{problem}. \\ $$

Question Number 67919 Answers: 0 Comments: 0

Question Number 67918 Answers: 1 Comments: 0

Question Number 68226 Answers: 0 Comments: 1

We are working on problems reported on post 67927. We will update on the resolution as soon as possible.

$$\mathrm{We}\:\mathrm{are}\:\mathrm{working}\:\mathrm{on}\:\mathrm{problems} \\ $$$$\mathrm{reported}\:\mathrm{on}\:\mathrm{post}\:\mathrm{67927}. \\ $$$$ \\ $$$$\mathrm{We}\:\mathrm{will}\:\mathrm{update}\:\mathrm{on}\:\mathrm{the}\:\mathrm{resolution} \\ $$$$\mathrm{as}\:\mathrm{soon}\:\mathrm{as}\:\mathrm{possible}. \\ $$

Question Number 67921 Answers: 0 Comments: 0

∫e^(y^2 /2) dy

$$\int{e}^{{y}^{\mathrm{2}} /\mathrm{2}} {dy} \\ $$

Question Number 67920 Answers: 0 Comments: 0

Question Number 67907 Answers: 1 Comments: 1

Question Number 67903 Answers: 2 Comments: 0

Question Number 67902 Answers: 0 Comments: 0

differential equation homogenous. please answer this.with p.s. xydx+2(x^2 +2y^2 )dy=0 x=0 y=1

$${differential}\:{equation} \\ $$$${homogenous}. \\ $$$$ \\ $$$${please}\:{answer}\:{this}.{with}\:{p}.{s}. \\ $$$${xydx}+\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} \right){dy}=\mathrm{0} \\ $$$${x}=\mathrm{0} \\ $$$${y}=\mathrm{1} \\ $$

Question Number 67900 Answers: 0 Comments: 0

homogenous differential equation. please answer. y(x^2 +xy−2y^2 )dx+x(3y^2 −xy−x^2 )2y=0 can someone answer this??

$${homogenous}\:{differential}\:{equation}. \\ $$$${please}\:{answer}. \\ $$$${y}\left({x}^{\mathrm{2}} +{xy}−\mathrm{2}{y}^{\mathrm{2}} \right){dx}+{x}\left(\mathrm{3}{y}^{\mathrm{2}} −{xy}−{x}^{\mathrm{2}} \right)\mathrm{2}{y}=\mathrm{0} \\ $$$$ \\ $$$${can}\:{someone}\:{answer}\:{this}?? \\ $$

Question Number 67899 Answers: 1 Comments: 2

homogenous differential equation. (2xy+y^2 )dr−2x^2 dy=0 y=e x=e

$${homogenous}\:{differential}\:{equation}. \\ $$$$ \\ $$$$\left(\mathrm{2}{xy}+{y}^{\mathrm{2}} \right){dr}−\mathrm{2}{x}^{\mathrm{2}} {dy}=\mathrm{0} \\ $$$${y}={e} \\ $$$${x}={e} \\ $$

Question Number 67898 Answers: 0 Comments: 0

differential equation. homogenous. ydx+(2x+3y)dy=0

$$ \\ $$$${differential}\:{equation}. \\ $$$${homogenous}. \\ $$$$ \\ $$$${ydx}+\left(\mathrm{2}{x}+\mathrm{3}{y}\right){dy}=\mathrm{0} \\ $$$$ \\ $$

Question Number 67881 Answers: 1 Comments: 0

find all x,y ∈R such that (x+yi)^(2019) =x−yi

$${find}\:{all}\:{x},{y}\:\in{R}\:{such}\:{that} \\ $$$$\left({x}+{yi}\right)^{\mathrm{2019}} ={x}−{yi} \\ $$

Question Number 67871 Answers: 1 Comments: 1

8=4x x=?

$$\mathrm{8}=\mathrm{4x} \\ $$$$\mathrm{x}=? \\ $$

Question Number 67860 Answers: 1 Comments: 3

Question Number 67852 Answers: 1 Comments: 4

Question Number 67851 Answers: 0 Comments: 5

find ∫ (dx/(x^2 −z)) with z from C .

$${find}\:\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{z}}\:\:{with}\:{z}\:{from}\:{C}\:. \\ $$

Question Number 67850 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) (dx/(x^2 −z)) with z from C

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{z}}\:\:{with}\:{z}\:{from}\:{C} \\ $$

Question Number 67849 Answers: 1 Comments: 7

Question Number 67844 Answers: 0 Comments: 2

x^2 +∣x∣−6=0

$${x}^{\mathrm{2}} +\mid{x}\mid−\mathrm{6}=\mathrm{0} \\ $$

Question Number 67836 Answers: 0 Comments: 0

If determinant ((x^n ,x^(n+2) ,x^(n+3) ),(y^n ,y^(n+2) ,y^(n+3) ),(z^n ,z^(n+2) ,z^(n+3) )) = (x−y)(y−z)(z−x)((1/x) + (1/y) + (1/z)), then n equals

$$\mathrm{If}\:\begin{vmatrix}{{x}^{{n}} }&{{x}^{{n}+\mathrm{2}} }&{{x}^{{n}+\mathrm{3}} }\\{{y}^{{n}} }&{{y}^{{n}+\mathrm{2}} }&{{y}^{{n}+\mathrm{3}} }\\{{z}^{{n}} }&{{z}^{{n}+\mathrm{2}} }&{{z}^{{n}+\mathrm{3}} }\end{vmatrix} \\ $$$$=\:\left({x}−{y}\right)\left({y}−{z}\right)\left({z}−{x}\right)\left(\frac{\mathrm{1}}{{x}}\:+\:\frac{\mathrm{1}}{{y}}\:+\:\frac{\mathrm{1}}{{z}}\right), \\ $$$$\mathrm{then}\:{n}\:\mathrm{equals} \\ $$

Question Number 67835 Answers: 1 Comments: 0

∫_0 ^2 x(8−x^3 )^(1/3) dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} {x}\left(\mathrm{8}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx} \\ $$

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