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Question Number 118588    Answers: 1   Comments: 1

x(x+y) dy −x^2 dx = 0

$${x}\left({x}+{y}\right)\:{dy}\:−{x}^{\mathrm{2}} \:{dx}\:=\:\mathrm{0}\: \\ $$

Question Number 118585    Answers: 0   Comments: 4

v2.227 reverts app first screen to two parts, saved and forum. To start in forum by default change settings and Enable start in forum. Non English users were having difficulty in locating offline editor. Work is in progress to translate in-app menu to different languages.

$${v}\mathrm{2}.\mathrm{227}\:\mathrm{reverts}\:\mathrm{app}\:\mathrm{first}\:\mathrm{screen}\:\mathrm{to} \\ $$$$\mathrm{two}\:\mathrm{parts},\:\mathrm{saved}\:\mathrm{and}\:\mathrm{forum}. \\ $$$$\mathrm{To}\:\mathrm{start}\:\mathrm{in}\:\mathrm{forum}\:\mathrm{by}\:\mathrm{default}\:\mathrm{change} \\ $$$$\mathrm{settings}\:\mathrm{and}\:\mathrm{Enable}\:\mathrm{start}\:\mathrm{in}\:\mathrm{forum}. \\ $$$$\mathrm{Non}\:\mathrm{English}\:\mathrm{users}\:\mathrm{were}\:\mathrm{having} \\ $$$$\mathrm{difficulty}\:\mathrm{in}\:\mathrm{locating}\:\mathrm{offline}\:\mathrm{editor}. \\ $$$$\mathrm{Work}\:\mathrm{is}\:\mathrm{in}\:\mathrm{progress}\:\mathrm{to}\:\mathrm{translate} \\ $$$$\mathrm{in}-\mathrm{app}\:\mathrm{menu}\:\mathrm{to}\:\mathrm{different}\:\mathrm{languages}. \\ $$

Question Number 118575    Answers: 1   Comments: 0

∫ cos (2cot^(−1) (√((1−x)/(1+x))) ) dx ?

$$\:\:\int\:\mathrm{cos}\:\left(\mathrm{2cot}^{−\mathrm{1}} \sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:\right)\:{dx}\:? \\ $$

Question Number 118574    Answers: 1   Comments: 0

find particular solution of (D^3 +4D) y = sin 2x by using inverse operation ?

$${find}\:{particular}\:{solution}\:{of}\: \\ $$$$\left({D}^{\mathrm{3}} +\mathrm{4}{D}\right)\:{y}\:=\:\mathrm{sin}\:\mathrm{2}{x}\:{by}\:{using} \\ $$$${inverse}\:{operation}\:? \\ $$

Question Number 118570    Answers: 2   Comments: 0

Find the dimensions of the largest rectangular garden that can be enclosed by 80m of fencing

$${Find}\:{the}\:{dimensions}\:{of}\:{the} \\ $$$${largest}\:{rectangular}\:{garden}\:{that} \\ $$$${can}\:{be}\:{enclosed}\:{by}\:\mathrm{80}{m}\:{of} \\ $$$${fencing} \\ $$

Question Number 118566    Answers: 6   Comments: 2

solve ∫_0 ^1 (dx/( (√x) (√(1−x)) )) .

$$\:\:{solve}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{{x}}\:\sqrt{\mathrm{1}−{x}}\:}\:. \\ $$

Question Number 118555    Answers: 2   Comments: 0

Question Number 118545    Answers: 1   Comments: 1

Question Number 118541    Answers: 3   Comments: 1

∫ tan (x).tan (2x).tan (3x) dx = ?

$$\:\:\:\int\:\mathrm{tan}\:\left({x}\right).\mathrm{tan}\:\left(\mathrm{2}{x}\right).\mathrm{tan}\:\left(\mathrm{3}{x}\right)\:{dx}\:=\:? \\ $$

Question Number 118546    Answers: 3   Comments: 7

nilai maksimum?fungsi y= 1+ sin 2x +cos 2x

$${nilai}\:{maksimum}?{fungsi}\:{y}=\:\mathrm{1}+\:{sin}\:\mathrm{2}{x}\:+{cos}\:\mathrm{2}{x} \\ $$

Question Number 118513    Answers: 2   Comments: 0

If f(x) + f(((x − 1)/x)) = 1 + x, find f(2).

$$\mathrm{If}\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:\:+\:\:\mathrm{f}\left(\frac{\mathrm{x}\:\:−\:\:\mathrm{1}}{\mathrm{x}}\right)\:\:\:=\:\:\:\mathrm{1}\:\:+\:\:\mathrm{x},\:\:\:\:\:\:\:\mathrm{find}\:\:\:\mathrm{f}\left(\mathrm{2}\right). \\ $$

Question Number 121164    Answers: 0   Comments: 0

...ADVANCED CALCULUS... If ∫_0 ^( ∞) ln(x)sin(x^2 )dx =λ∫_0 ^( ∞) sin(x^2 )dx then find the value of ′′λ′′ . ...m.n.july.1970...

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\mathrm{ADVANCED}\:\:\mathrm{CALCULUS}... \\ $$$$\:\:\:\:\mathrm{If}\:\:\:\int_{\mathrm{0}} ^{\:\infty} {ln}\left({x}\right){sin}\left({x}^{\mathrm{2}} \right){dx}\:=\lambda\int_{\mathrm{0}} ^{\:\infty} {sin}\left({x}^{\mathrm{2}} \right){dx}\: \\ $$$$\:\:\:\:\:\:\:\:{then}\:\:{find}\:\:{the}\:\:{value}\:{of}\:''\lambda''\:. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\mathrm{m}.\mathrm{n}.\mathrm{july}.\mathrm{1970}... \\ $$

Question Number 118506    Answers: 2   Comments: 0

Question Number 118511    Answers: 3   Comments: 0

How many positive integers x satisfy log_(x/8) (x^2 /4)<7+log_2 (8/x)

$$\mathrm{How}\:\mathrm{many}\:\mathrm{positive}\:\mathrm{integers}\:{x}\:\mathrm{satisfy} \\ $$$$\mathrm{log}_{\frac{{x}}{\mathrm{8}}} \frac{{x}^{\mathrm{2}} }{\mathrm{4}}<\mathrm{7}+\mathrm{log}_{\mathrm{2}} \frac{\mathrm{8}}{{x}} \\ $$

Question Number 118491    Answers: 1   Comments: 0

... ⧫Advanced Calculus⧫... Evaluate:: Ω = ∫_0 ^( ∞) ((secθ)/( (√(4tan^2 θ+5))))dθ ...♠L𝛗rD ∅sE♠... ...♣GooD LucK♣

$$ \\ $$$$...\:\blacklozenge\mathrm{Advanced}\:\mathrm{Calculus}\blacklozenge... \\ $$$$ \\ $$$$\mathrm{Evaluate}:: \\ $$$$ \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sec}\theta}{\:\sqrt{\mathrm{4tan}^{\mathrm{2}} \theta+\mathrm{5}}}\mathrm{d}\theta \\ $$$$ \\ $$$$...\spadesuit\boldsymbol{\mathrm{L}\phi\mathrm{rD}}\:\boldsymbol{\varnothing\mathrm{sE}}\spadesuit... \\ $$$$ \\ $$$$...\clubsuit\boldsymbol{\mathrm{GooD}}\:\boldsymbol{\mathrm{LucK}}\clubsuit \\ $$

Question Number 118489    Answers: 2   Comments: 0

(1) solve the equation ((x−49)/(50)) + ((x−50)/(49)) = ((49)/(x−50)) + ((50)/(x−49)) (2) How many numbers from 12 to 12345 inclusive have digits which are consecutive an in increasing order, reading from left to right ?

$$\left(\mathrm{1}\right)\:{solve}\:{the}\:{equation}\:\frac{{x}−\mathrm{49}}{\mathrm{50}}\:+\:\frac{{x}−\mathrm{50}}{\mathrm{49}}\:=\:\frac{\mathrm{49}}{{x}−\mathrm{50}}\:+\:\frac{\mathrm{50}}{{x}−\mathrm{49}} \\ $$$$\left(\mathrm{2}\right)\:{How}\:{many}\:{numbers}\:{from}\:\mathrm{12}\:{to}\:\mathrm{12345}\: \\ $$$${inclusive}\:{have}\:{digits}\:{which}\:{are}\: \\ $$$${consecutive}\:{an}\:{in}\:{increasing}\:{order}, \\ $$$${reading}\:{from}\:{left}\:{to}\:{right}\:?\: \\ $$

Question Number 118488    Answers: 1   Comments: 0

Conjecture a formula for the infinite sum of the series. (1/3)+(1/(15))+(1/(35))+ ∙ ∙ ∙ (1/((2n−1)(2n+1))) And prove the formula by Induction.

$$\boldsymbol{\mathrm{Conjecture}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{formula}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{infinite}} \\ $$$$\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{series}}. \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{15}}+\frac{\mathrm{1}}{\mathrm{35}}+\:\centerdot\:\centerdot\:\centerdot\:\frac{\mathrm{1}}{\left(\mathrm{2}\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)} \\ $$$$\boldsymbol{\mathrm{And}}\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{formula}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{Induction}}. \\ $$

Question Number 118482    Answers: 1   Comments: 0

If the tangents at the end of a focal chord of parabola meet the tangent at the vertex in C,D.prove that CD substends a right angle at the focus

$$\mathrm{If}\:\mathrm{the}\:\mathrm{tangents}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{end}\:\mathrm{of}\:\mathrm{a}\:\mathrm{focal}\:\:\mathrm{chord}\:\mathrm{of} \\ $$$$\mathrm{parabola}\:\mathrm{meet}\:\mathrm{the} \\ $$$$\mathrm{tangent}\:\mathrm{at}\:\mathrm{the}\:\:\mathrm{vertex} \\ $$$$\mathrm{in}\:\mathrm{C},\mathrm{D}.\mathrm{prove}\:\mathrm{that}\:\mathrm{CD} \\ $$$$\mathrm{substends}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angle} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{focus} \\ $$

Question Number 118478    Answers: 0   Comments: 0

find ∫_0 ^∞ e^(−2x) ln(1+3x)dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{2x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{3x}\right)\mathrm{dx} \\ $$

Question Number 118476    Answers: 0   Comments: 0

find ∫_(−∞) ^∞ ((arctan(1+2x))/(x^2 +1))dx

$$\mathrm{find}\:\int_{−\infty} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{1}+\mathrm{2x}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 118475    Answers: 0   Comments: 0

calculate ∫_0 ^∞ ((arctan(2+x^2 ))/(x^2 +9))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{2}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{9}}\mathrm{dx} \\ $$

Question Number 118466    Answers: 2   Comments: 0

solve ∫_0 ^1 ((tan^(−1) x)/(√(1−x^2 )))dx

$${solve} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{tan}^{−\mathrm{1}} {x}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 118455    Answers: 6   Comments: 1

Question Number 118452    Answers: 2   Comments: 3

Question: 2^x +2^(2x+1) +1=y^2 solve this equation if x,y𝛆Z

$$\boldsymbol{{Question}}: \\ $$$$\mathrm{2}^{\boldsymbol{{x}}} +\mathrm{2}^{\mathrm{2}\boldsymbol{{x}}+\mathrm{1}} +\mathrm{1}=\boldsymbol{{y}}^{\mathrm{2}} \:\:\:\boldsymbol{{solve}}\:\boldsymbol{{this}}\:\boldsymbol{{equation}}\:\boldsymbol{{if}} \\ $$$$\boldsymbol{{x}},\boldsymbol{{y}\epsilon}\mathbb{Z} \\ $$

Question Number 118448    Answers: 3   Comments: 0

Question Number 118442    Answers: 1   Comments: 0

sin x.y′′ +2cos x. y′−y sin x = e^x

$$\:\:\mathrm{sin}\:{x}.{y}''\:+\mathrm{2cos}\:{x}.\:{y}'−{y}\:\mathrm{sin}\:{x}\:=\:{e}^{{x}} \\ $$$$ \\ $$

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