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Question Number 47852    Answers: 0   Comments: 1

1) find ∫ x arctan(x)dx 2) find the value of ∫_0 ^1 x arctan(x)dx

$$\left.\mathrm{1}\right)\:{find}\:\int\:{x}\:{arctan}\left({x}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}\:{arctan}\left({x}\right){dx} \\ $$

Question Number 47851    Answers: 2   Comments: 3

let f(x)=x+1+(√x) and g(x)=x+1−(√x) find ∫ ((f(x))/(g(x)))dx and ((∫f(x)dx)/(∫g(x)dx)) .

$${let}\:\:{f}\left({x}\right)={x}+\mathrm{1}+\sqrt{{x}}\:{and}\:{g}\left({x}\right)={x}+\mathrm{1}−\sqrt{{x}} \\ $$$${find}\:\int\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}{dx}\:\:{and}\:\:\frac{\int{f}\left({x}\right){dx}}{\int{g}\left({x}\right){dx}}\:. \\ $$

Question Number 47848    Answers: 0   Comments: 2

A body ascends a slope with a speed of 10m/s.If 105J of energy of the body is lost due to friction then the height to which the body will rise is a)0.5m b)4.5m c)3.5m d)2.0m

$${A}\:{body}\:{ascends}\:{a}\:{slope}\:{with}\:{a} \\ $$$${speed}\:{of}\:\mathrm{10}{m}/{s}.{If}\:\mathrm{105}{J}\:{of}\:{energy} \\ $$$${of}\:{the}\:{body}\:{is}\:{lost}\:{due}\:{to}\:{friction}\: \\ $$$${then}\:{the}\:{height}\:{to}\:{which}\:{the}\:{body} \\ $$$${will}\:{rise}\:{is} \\ $$$$\left.{a}\left.\right)\left.\mathrm{0}\left..\mathrm{5}{m}\:\:\:{b}\right)\mathrm{4}.\mathrm{5}{m}\:\:\:{c}\right)\mathrm{3}.\mathrm{5}{m}\:\:\:{d}\right)\mathrm{2}.\mathrm{0}{m} \\ $$

Question Number 47837    Answers: 0   Comments: 0

there are 5 possible answers for each question of a multiple choice exam containing 10 questions. if a condidate answered it randomly. find the probability that he gets (i) no question right (ii) 3 questions right (iii) 5 questions right (iv) at least one question right

$${there}\:{are}\:\mathrm{5}\:{possible}\:{answers}\:{for}\:{each}\:{question}\:{of}\:{a}\: \\ $$$${multiple}\:{choice}\:{exam}\:{containing}\:\mathrm{10}\:{questions}.\: \\ $$$${if}\:{a}\:{condidate}\:{answered}\:{it}\:{randomly}.\: \\ $$$${find}\:{the}\:{probability}\:{that}\:{he}\:{gets}\:\left({i}\right)\:{no}\:{question}\:{right} \\ $$$$\:\left({ii}\right)\:\mathrm{3}\:{questions}\:{right}\:\left({iii}\right)\:\mathrm{5}\:{questions}\:{right}\: \\ $$$$\:\left({iv}\right)\:{at}\:{least}\:{one}\:{question}\:{right}\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 47836    Answers: 2   Comments: 0

prove cosec^2 θ−cotθcosecθ=1

$${prove}\:{cosec}^{\mathrm{2}} \theta−{cot}\theta{cosec}\theta=\mathrm{1} \\ $$

Question Number 47831    Answers: 2   Comments: 1

Question Number 47824    Answers: 2   Comments: 2

Question Number 47821    Answers: 1   Comments: 0

L_1 and L_2 are two lines which intersects each other at a right angle at the point (1,3),L_1 cuts the y−axis at the point (0,2) find the equations of L_1 and L_2

$$\boldsymbol{\mathrm{L}}_{\mathrm{1}} \boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{L}}_{\mathrm{2}} \:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{lines}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{intersects}} \\ $$$$\boldsymbol{\mathrm{each}}\:\boldsymbol{\mathrm{other}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{right}}\:\boldsymbol{\mathrm{angle}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{point}}\:\left(\mathrm{1},\mathrm{3}\right),\boldsymbol{\mathrm{L}}_{\mathrm{1}} \:\boldsymbol{\mathrm{cuts}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{axis}}\:\boldsymbol{\mathrm{at}} \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{point}}\:\left(\mathrm{0},\mathrm{2}\right)\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{equations}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{L}}_{\mathrm{1}} \boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{L}}_{\mathrm{2}} \\ $$$$ \\ $$

Question Number 47817    Answers: 1   Comments: 1

Question Number 47815    Answers: 1   Comments: 3

Question Number 47814    Answers: 1   Comments: 1

A boy runs towards a man standing 150m away.Speed of boy is 5m/s and that of man is 10m/s.The time and distance of their meeting from the boy^. s position are a)15s b)5s and 150m c)10s and 50m d)10s and 100m

$${A}\:{boy}\:{runs}\:{towards}\:{a}\:{man}\:{standing} \\ $$$$\mathrm{150}{m}\:{away}.{Speed}\:{of}\:{boy}\:{is}\:\mathrm{5}{m}/{s} \\ $$$${and}\:{that}\:{of}\:{man}\:{is}\:\mathrm{10}{m}/{s}.{The} \\ $$$${time}\:{and}\:{distance}\:{of}\:{their}\:{meeting} \\ $$$${from}\:{the}\:{boy}^{.} {s}\:{position}\:{are} \\ $$$$\left.{a}\left.\right)\left.\mathrm{15}{s}\:{b}\right)\mathrm{5}{s}\:{and}\:\mathrm{150}{m}\:{c}\right)\mathrm{10}{s}\:{and}\:\mathrm{50}{m} \\ $$$$\left.{d}\right)\mathrm{10}{s}\:{and}\:\mathrm{100}{m} \\ $$

Question Number 47807    Answers: 1   Comments: 0

sin xy^2 =y^2 +2x diferential express is

$$\mathrm{sin}\:{xy}^{\mathrm{2}} ={y}^{\mathrm{2}} +\mathrm{2}{x} \\ $$$$ \\ $$$$\mathrm{diferential}\:{express}\:\mathrm{is} \\ $$

Question Number 47850    Answers: 1   Comments: 2

calculate A_p =∫_0 ^1 ((x^p −1)/(ln(x)))dx with p>0.

$${calculate}\:{A}_{{p}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{{p}} −\mathrm{1}}{{ln}\left({x}\right)}{dx}\:{with}\:{p}>\mathrm{0}. \\ $$

Question Number 47788    Answers: 0   Comments: 1

Question Number 47779    Answers: 0   Comments: 1

Question Number 47778    Answers: 1   Comments: 0

f(x)=2x^3 +x^2 −2x−1 f^(−1) (x)=...

$${f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=... \\ $$

Question Number 47775    Answers: 2   Comments: 1

Question Number 47771    Answers: 0   Comments: 0

∫_0 ^(π/2) (x/(tanx))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}}{{tanx}}{dx} \\ $$

Question Number 47770    Answers: 1   Comments: 3

∫_0 ^1 ((x^2 −1)/(lnx))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}} −\mathrm{1}}{{lnx}}{dx} \\ $$

Question Number 47768    Answers: 0   Comments: 3

Somebody know spanish?

$$\mathrm{Somebody}\:\mathrm{know}\:\mathrm{spanish}? \\ $$

Question Number 47810    Answers: 1   Comments: 1

A mobike rider moving from A to B with speed 20km/h notices that a bus goes past it every 21 minute in the direction of his motion and every 7 minutes in the opposite direction.Velocity of the bus is a)25km/h b)35km/h c)30km/h d)40km/h

$${A}\:{mobike}\:{rider}\:{moving}\:{from}\:{A}\:{to}\:{B} \\ $$$${with}\:{speed}\:\mathrm{20}{km}/{h}\:{notices}\:{that}\:{a} \\ $$$${bus}\:{goes}\:{past}\:{it}\:{every}\:\mathrm{21}\:{minute}\:{in} \\ $$$${the}\:{direction}\:{of}\:{his}\:{motion}\:{and} \\ $$$${every}\:\mathrm{7}\:{minutes}\:{in}\:{the}\:{opposite} \\ $$$${direction}.{Velocity}\:{of}\:{the}\:{bus}\:{is} \\ $$$$\left.{a}\left.\right)\left.\mathrm{25}{km}/{h}\:{b}\right)\mathrm{35}{km}/{h}\:{c}\right)\mathrm{30}{km}/{h} \\ $$$$\left.{d}\right)\mathrm{40}{km}/{h} \\ $$$$ \\ $$

Question Number 47743    Answers: 2   Comments: 0

∫(dx/(x^n −x)) the problems i have posted are tricky...

$$\int\frac{{dx}}{{x}^{{n}} −{x}}\:\: \\ $$$${the}\:{problems}\:{i}\:{have}\:{posted}\:{are}\:{tricky}... \\ $$

Question Number 47737    Answers: 1   Comments: 0

I = ∫_0 ^( L/2) ((Rz^2 )/((d^2 +z^2 )(√(d^2 +z^2 −R^2 )))) dz Find I .

$$\:\:{I}\:=\:\int_{\mathrm{0}} ^{\:\:{L}/\mathrm{2}} \frac{{Rz}^{\mathrm{2}} }{\left({d}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)\sqrt{{d}^{\mathrm{2}} +{z}^{\mathrm{2}} −{R}^{\mathrm{2}} }}\:{dz} \\ $$$$\:{Find}\:{I}\:. \\ $$

Question Number 47735    Answers: 1   Comments: 5

Question Number 47727    Answers: 1   Comments: 0

Find the value of a for a : 4 : : 5 : 10

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{a}\:\mathrm{for} \\ $$$$\:\:\:\:\:{a}\::\:\mathrm{4}\::\::\:\mathrm{5}\::\:\mathrm{10} \\ $$

Question Number 47725    Answers: 1   Comments: 2

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