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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

Question Number 47713 Answers: 0 Comments: 4

Question Number 47712 Answers: 0 Comments: 0

show that ^(^2 C_2 ) C_n = (1/((1−n)!(n−1)(n−2)(n−3)...3(2)(1)))

$${show}\:{that}\: \\ $$$$\:\:^{\:^{\mathrm{2}} \:{C}_{\mathrm{2}} \:} {C}_{{n}} =\:\frac{\mathrm{1}}{\left(\mathrm{1}−{n}\right)!\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)\left({n}−\mathrm{3}\right)...\mathrm{3}\left(\mathrm{2}\right)\left(\mathrm{1}\right)} \\ $$

Question Number 47720 Answers: 2 Comments: 0

find ∫ ln(1+x^3 )dx

$${find}\:\int\:{ln}\left(\mathrm{1}+{x}^{\mathrm{3}} \right){dx} \\ $$

Question Number 47740 Answers: 2 Comments: 0

∫(dx/(x(x+1)(x+2)(x+3)...(x+n)))

$$\int\frac{{dx}}{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)...\left({x}+{n}\right)} \\ $$

Question Number 47697 Answers: 1 Comments: 1

Question Number 47677 Answers: 0 Comments: 3

∫x^(x ) dx=

$$\int\mathrm{x}^{\mathrm{x}\:} \mathrm{dx}= \\ $$

Question Number 47675 Answers: 2 Comments: 0

A particle of mass 4kg was at rest a a point of position vector i +4j. A force F was applied to it and it moved at a velocity of (3i + 7j)ms^(−1) after a time of 5seconds. Find a) the magnitude of F b) The speed at which it moves,Hence, c) The distance it covered.

$${A}\:{particle}\:{of}\:{mass}\:\mathrm{4}{kg}\:{was}\:{at}\:{rest}\:{a}\:{a}\:{point}\:{of}\:{position}\:{vector} \\ $$$${i}\:+\mathrm{4}{j}.\:{A}\:{force}\:{F}\:{was}\:{applied}\:{to}\:{it}\:{and}\:{it}\:{moved}\:{at}\:{a}\:{velocity} \\ $$$${of}\:\left(\mathrm{3}{i}\:+\:\mathrm{7}{j}\right){ms}^{−\mathrm{1}} \:\:\:{after}\:{a}\:{time}\:{of}\:\:\mathrm{5}{seconds}.\:{Find}\: \\ $$$$\left.{a}\right)\:{the}\:{magnitude}\:{of}\:{F} \\ $$$$\left.{b}\right)\:{The}\:{speed}\:{at}\:{which}\:{it}\:{moves},{Hence}, \\ $$$$\left.{c}\right)\:{The}\:{distance}\:{it}\:{covered}. \\ $$$$ \\ $$$$ \\ $$

Question Number 47659 Answers: 2 Comments: 0

Question Number 47657 Answers: 1 Comments: 7

Question Number 47656 Answers: 1 Comments: 1

A square is divided into 9 identical smaller squares.Six identical balls are to be placed in these smaller squares such that each of the three rows gets at least one ball(one ball in one square only).In how many different ways can this be done? a)91 b)51 c)81 d)41

$${A}\:{square}\:{is}\:{divided}\:{into}\:\mathrm{9}\:{identical} \\ $$$${smaller}\:{squares}.{Six}\:{identical}\:{balls} \\ $$$${are}\:{to}\:{be}\:{placed}\:{in}\:{these}\:{smaller}\: \\ $$$${squares}\:{such}\:{that}\:{each}\:{of}\:{the}\:{three} \\ $$$${rows}\:{gets}\:{at}\:{least}\:{one}\:{ball}\left({one}\right. \\ $$$$\left.{ball}\:{in}\:{one}\:{square}\:{only}\right).{In}\:{how} \\ $$$${many}\:{different}\:{ways}\:{can}\:{this}\:{be} \\ $$$${done}? \\ $$$$\left.{a}\left.\right)\left.\mathrm{9}\left.\mathrm{1}\:{b}\right)\mathrm{51}\:{c}\right)\mathrm{81}\:{d}\right)\mathrm{41} \\ $$$$ \\ $$

Question Number 47651 Answers: 1 Comments: 1

calculate A_n =∫_0 ^1 sin([nx])e^(−2x) dx with n integr natural .

$${calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{sin}\left(\left[{nx}\right]\right){e}^{−\mathrm{2}{x}} {dx}\:{with}\:{n} \\ $$$${integr}\:{natural}\:. \\ $$

Question Number 47646 Answers: 1 Comments: 2

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