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Question Number 42487    Answers: 0   Comments: 3

let f(x) = ∫_0 ^1 (dt/(x +ch(t))) 1) find a explicite form of f(x) 2) calculate ∫_0 ^1 (dt/((x+ch(t))^2 )) 3) find the value of ∫_0 ^1 (dt/(1+ch(t))) and ∫_0 ^1 (dt/(2+ch(t))) 4) find the value of ∫_0 ^1 (dt/((1+cht)^2 )) and ∫_0 ^1 (dt/((2+cht)^2 ))

$${let}\:\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\:\frac{{dt}}{{x}\:+{ch}\left({t}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicite}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\left({x}+{ch}\left({t}\right)\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\frac{{dt}}{\mathrm{1}+{ch}\left({t}\right)}\:{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{2}+{ch}\left({t}\right)} \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{cht}\right)^{\mathrm{2}} }\:\:{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{\left(\mathrm{2}+{cht}\right)^{\mathrm{2}} } \\ $$

Question Number 42479    Answers: 1   Comments: 0

two digit number is seven times the sum of its digits.if 27 is substracted from the number its digits get interchanged. find the number

$$\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{digit}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{seven}}\:\boldsymbol{\mathrm{times}}\: \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{digits}}.\boldsymbol{\mathrm{if}}\:\mathrm{27}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{substracted}}\: \\ $$$$\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{digits}}\:\boldsymbol{\mathrm{get}}\:\boldsymbol{\mathrm{interchanged}}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}} \\ $$$$ \\ $$

Question Number 42481    Answers: 0   Comments: 0

find f(x)= ∫_0 ^(π/4) ln(1+xtant)dt .

$${find}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+{xtant}\right){dt}\:. \\ $$

Question Number 42482    Answers: 0   Comments: 3

let f(x)=e^(−2x) arctan(x) 1) calculate f^((n)) (x) 2) calculate f^((n)) (0) 3) developp f at integr serie .

$${let}\:{f}\left({x}\right)={e}^{−\mathrm{2}{x}} \:{arctan}\left({x}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 42475    Answers: 0   Comments: 1

A signpost 4.5cm high is 30cm away⊛ from Mrs Rahup.What is the height of the image formed in her retina?(Take the eye lens-retina distance as 1.5cm).

$${A}\:{signpost}\:\mathrm{4}.\mathrm{5}{cm}\:{high}\:{is}\:\mathrm{30}{cm}\:{away}\circledast \\ $$$${from}\:{Mrs}\:{Rahup}.{What}\:{is}\:{the} \\ $$$${height}\:{of}\:{the}\:{image}\:{formed}\:{in}\:{her} \\ $$$${retina}?\left({Take}\:{the}\:{eye}\:{lens}-{retina}\right. \\ $$$$\left.{distance}\:{as}\:\mathrm{1}.\mathrm{5}{cm}\right). \\ $$

Question Number 42474    Answers: 0   Comments: 0

Question Number 42473    Answers: 0   Comments: 0

Question Number 42472    Answers: 0   Comments: 0

Question Number 42471    Answers: 0   Comments: 0

Question Number 42470    Answers: 0   Comments: 0

Question Number 42469    Answers: 0   Comments: 0

Question Number 42468    Answers: 0   Comments: 0

Question Number 42463    Answers: 1   Comments: 1

let y =(√(x+(√(x+(√(x+2)))))) calculate (dy/dx)

$${let}\:{y}\:\:=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\mathrm{2}}}} \\ $$$${calculate}\:\:\frac{{dy}}{{dx}} \\ $$

Question Number 42458    Answers: 0   Comments: 0

a boy is in front of a wall.The distance between boy and wall is 12ft.the boy is moving towards the wall in such a way that half the distance between the wall and him is crossed in one minutes.So find the time the boy reach to the wall

$${a}\:{boy}\:{is}\:{in}\:{front}\:{of}\:{a}\:{wall}.{The}\:{distance}\:{between} \\ $$$${boy}\:{and}\:{wall}\:{is}\:\mathrm{12}{ft}.{the}\:{boy}\:{is}\:{moving}\:{towards} \\ $$$${the}\:{wall}\:{in}\:{such}\:{a}\:{way}\:{that}\:\boldsymbol{{half}}\:\boldsymbol{{the}}\:\boldsymbol{{distance}} \\ $$$$\boldsymbol{{between}}\:\boldsymbol{{the}}\:\boldsymbol{{wall}}\:\boldsymbol{{and}}\:\boldsymbol{{him}}\:\boldsymbol{{is}}\:\boldsymbol{{crossed}}\:\boldsymbol{{in}}\:\boldsymbol{{one}} \\ $$$$\boldsymbol{{minutes}}.\boldsymbol{{S}}{o}\:{find}\:{the}\:{time}\:{the}\:{boy}\:{reach}\:{to}\:{the}\:{wall} \\ $$

Question Number 42448    Answers: 3   Comments: 0

Question Number 42446    Answers: 2   Comments: 1

Question Number 42445    Answers: 0   Comments: 0

find A_n = ∫_0 ^(π/4) tan^n t dt with n integer natural .

$${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{tan}^{{n}} {t}\:{dt}\:\:\:{with}\:{n}\:{integer}\:{natural}\:. \\ $$

Question Number 42435    Answers: 1   Comments: 1

find ∫_0 ^1 (dx/((√x) +(√(1−x))))

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{\sqrt{{x}}\:+\sqrt{\mathrm{1}−{x}}} \\ $$

Question Number 42430    Answers: 1   Comments: 2

find ∫ (dx/(3+tan^2 x))

$${find}\:\int\:\:\:\:\:\:\:\frac{{dx}}{\mathrm{3}+{tan}^{\mathrm{2}} {x}} \\ $$

Question Number 42422    Answers: 1   Comments: 2

Question Number 42408    Answers: 0   Comments: 2

(√(a−(√(a+x ))))+ (√(a+(√(a−x)) )) = 2x Solve for x in terms of a

$$\sqrt{{a}−\sqrt{{a}+{x}\:}}+\:\sqrt{{a}+\sqrt{{a}−{x}}\:}\:=\:\mathrm{2}{x} \\ $$$${Solve}\:{for}\:{x}\:{in}\:{terms}\:{of}\:{a} \\ $$

Question Number 42407    Answers: 1   Comments: 1

∫ (1/(1 + tanx)) dx

$$\int\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{tanx}}\:\mathrm{dx} \\ $$

Question Number 42402    Answers: 0   Comments: 0

calculate ∫∫_(x≤x^2 +y^2 ≤1) ((dxdy)/((1+x^2 +y^2 )^2 ))

$${calculate}\:\int\int_{{x}\leqslant{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant\mathrm{1}} \:\:\:\frac{{dxdy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$

Question Number 42395    Answers: 0   Comments: 1

calculate ∫∫_D ((xy)/((1+x^2 +y^2 )))dxdy with D ={(x,y)∈ R^2 / 0≤x≤1 ,0≤y≤1, x^2 +y^2 ≤1}

$${calculate}\:\int\int_{{D}} \:\:\:\:\:\:\frac{{xy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)}{dxdy}\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in\:{R}^{\mathrm{2}} \:\:/\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\mathrm{0}\leqslant{y}\leqslant\mathrm{1},\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{1}\right\} \\ $$

Question Number 42394    Answers: 1   Comments: 1

find ∫_0 ^1 (dt/(t+(√(1−t^2 )))) dt

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{t}+\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}\:{dt} \\ $$

Question Number 42392    Answers: 1   Comments: 1

calculate ∫ ((lnx)/(x +x(lnx)^2 ))dx

$${calculate}\:\int\:\:\:\frac{{lnx}}{{x}\:+{x}\left({lnx}\right)^{\mathrm{2}} }{dx} \\ $$

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