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Question Number 86480    Answers: 0   Comments: 1

∫_0 ^∞ (x e^(1−x) −⌊x⌋e^(1−⌊x⌋) )dx

$$\int_{\mathrm{0}} ^{\infty} \left({x}\:{e}^{\mathrm{1}−{x}} \:−\lfloor{x}\rfloor{e}^{\mathrm{1}−\lfloor{x}\rfloor} \right){dx} \\ $$

Question Number 86479    Answers: 1   Comments: 0

a ball is droped from a height 20 m. Given that it rebounce with a velocity of (3/4) that which it hit the ground find the time interval between the first and second rebounce.

$$\mathrm{a}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{droped}\:\mathrm{from}\:\mathrm{a}\:\mathrm{height}\:\mathrm{20}\:\mathrm{m}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{it} \\ $$$$\mathrm{rebounce}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{that}\:\mathrm{which}\:\mathrm{it}\:\mathrm{hit}\:\mathrm{the}\:\mathrm{ground} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{time}\:\mathrm{interval}\:\mathrm{between}\:\mathrm{the}\:\mathrm{first}\:\mathrm{and}\:\mathrm{second}\:\mathrm{rebounce}. \\ $$

Question Number 86476    Answers: 0   Comments: 1

show that sin^(−1) α=−i ln (α±(√(α^2 −1)))−(π/2)

$$\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{sin}^{−\mathrm{1}} \alpha=−{i}\:\mathrm{ln}\:\left(\alpha\pm\sqrt{\alpha^{\mathrm{2}} −\mathrm{1}}\right)−\frac{\pi}{\mathrm{2}} \\ $$

Question Number 86472    Answers: 1   Comments: 0

Question Number 86461    Answers: 3   Comments: 0

Use exponential representation of sin θ and cos θ to show that a) sin^2 θ + cos^2 θ = 1 b) cos^2 θ − sin^2 θ = cos2θ c) 2 sinθ cosθ = 2sin2θ.

$$\mathrm{Use}\:\mathrm{exponential}\:\mathrm{representation}\:\mathrm{of}\:\mathrm{sin}\:\theta\:\mathrm{and}\:\mathrm{cos}\:\theta\:\mathrm{to}\:\mathrm{show}\:\mathrm{that} \\ $$$$\left.\mathrm{a}\left.\right)\:\mathrm{sin}^{\mathrm{2}} \:\theta\:+\:\mathrm{cos}^{\mathrm{2}} \:\theta\:=\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}\right)\:\mathrm{cos}^{\mathrm{2}} \theta\:−\:\mathrm{sin}^{\mathrm{2}} \theta\:=\:\mathrm{cos2}\theta \\ $$$$\left.\mathrm{c}\right)\:\mathrm{2}\:\mathrm{sin}\theta\:\mathrm{cos}\theta\:=\:\mathrm{2sin2}\theta. \\ $$

Question Number 86496    Answers: 0   Comments: 2

The number of integral terms in the expansion of (5^(1/2) + 7^(1/8) )^(1024) is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integral}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\:\:\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{2}}} +\:\mathrm{7}^{\frac{\mathrm{1}}{\mathrm{8}}} \right)^{\mathrm{1024}} \:\mathrm{is} \\ $$

Question Number 86454    Answers: 1   Comments: 0

pls check the question below

$$\:{pls}\:{check}\:{the}\: \\ $$$${question}\:{below} \\ $$

Question Number 86453    Answers: 1   Comments: 3

Question Number 86447    Answers: 0   Comments: 1

Question Number 86431    Answers: 2   Comments: 0

∫(√(x−(√(x^2 +1)) )) dx

$$\int\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:}\:{dx} \\ $$

Question Number 86428    Answers: 0   Comments: 2

∫ (dx/(a cos x + b sin x))?

$$\int\:\:\frac{\mathrm{dx}}{\mathrm{a}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{b}\:\mathrm{sin}\:\mathrm{x}}? \\ $$

Question Number 86426    Answers: 2   Comments: 0

solve in R x^3 −5=[x]

$${solve}\:{in}\:{R} \\ $$$${x}^{\mathrm{3}} −\mathrm{5}=\left[{x}\right] \\ $$

Question Number 86416    Answers: 0   Comments: 1

(√(8=)) 68]

$$\sqrt{\mathrm{8}=} \\ $$$$\left.\mathrm{68}\right] \\ $$$$ \\ $$

Question Number 86407    Answers: 1   Comments: 1

Question Number 86406    Answers: 2   Comments: 0

let u^→ =i^→ −j^→ +k^→ and v^→ =2i^→ +j^→ +3k^→ (o,i,j,k) orthonormal 1) calculate ∣∣u^→ ∣∣ ,∣∣v^→ ∣∣ ,u^→ .v^→ 2) calculate cos(u^→ ,v^→ ) 3)calculate u^→ Λv^→ and sin(u^→ ,v^→ )

$${let}\:\:\overset{\rightarrow} {{u}}=\overset{\rightarrow} {{i}}−\overset{\rightarrow} {{j}}\:+\overset{\rightarrow} {{k}}\:{and}\:\overset{\rightarrow} {{v}}=\mathrm{2}\overset{\rightarrow} {{i}}+\overset{\rightarrow} {{j}}\:+\mathrm{3}\overset{\rightarrow} {{k}} \\ $$$$\left({o},{i},{j},{k}\right)\:{orthonormal} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:\mid\mid\overset{\rightarrow} {{u}}\mid\mid\:\:,\mid\mid\overset{\rightarrow} {{v}}\mid\mid\:\:,\overset{\rightarrow} {{u}}.\overset{\rightarrow} {{v}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{cos}\left(\overset{\rightarrow} {{u}},\overset{\rightarrow} {{v}}\right) \\ $$$$\left.\mathrm{3}\right){calculate}\:\overset{\rightarrow} {{u}}\Lambda\overset{\rightarrow} {{v}}\:\:\:\:{and}\:\:{sin}\left(\overset{\rightarrow} {{u}},\overset{\rightarrow} {{v}}\right) \\ $$

Question Number 86405    Answers: 1   Comments: 2

Question Number 86399    Answers: 2   Comments: 3

Question Number 86397    Answers: 2   Comments: 2

∫(dx/(sin^2 (x)+tan^2 (x))) dx

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

Question Number 86396    Answers: 0   Comments: 0

Question Number 86379    Answers: 1   Comments: 2

Question Number 86375    Answers: 1   Comments: 2

calculate by complex method ∫_0 ^∞ (dx/(x^2 −x+1))

$${calculate}\:{by}\:{complex}\:{method}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}} \\ $$

Question Number 86365    Answers: 0   Comments: 0

I think it will be ∫_0 ^(π/4) (dx/(√(1+tanx))) ≈∫_0 ^(π/4) (dx/(√(1+x))) =(𝛑/4)−(1/2).(1/2).((𝛑/4))^2 +((1.3)/(2.4)).(1/3).((𝛑/4))^3 −((1.3.5)/(2.4.6)).(1/4)((𝛑/4))^4 +....

$$\mathrm{I}\:\mathrm{think}\:\mathrm{it}\:\mathrm{will}\:\mathrm{be} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{dx}}{\sqrt{\mathrm{1}+\mathrm{tanx}}}\:\approx\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{dx}}{\sqrt{\mathrm{1}+\mathrm{x}}}\: \\ $$$$=\frac{\boldsymbol{\pi}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{1}}{\mathrm{2}}.\left(\frac{\boldsymbol{\pi}}{\mathrm{4}}\right)^{\mathrm{2}} +\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}.\mathrm{4}}.\frac{\mathrm{1}}{\mathrm{3}}.\left(\frac{\boldsymbol{\pi}}{\mathrm{4}}\right)^{\mathrm{3}} −\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}.\mathrm{4}.\mathrm{6}}.\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\boldsymbol{\pi}}{\mathrm{4}}\right)^{\mathrm{4}} +.... \\ $$

Question Number 86361    Answers: 0   Comments: 2

mr.w can you check question no.76808

$${mr}.{w}\:{can}\:{you}\:{check} \\ $$$${question}\:{no}.\mathrm{76808} \\ $$

Question Number 86358    Answers: 0   Comments: 1

Question Number 86356    Answers: 1   Comments: 1

Question Number 86349    Answers: 0   Comments: 1

mr.aliesam can you check the answer of 76808

$${mr}.{aliesam}\:{can}\:{you} \\ $$$${check}\:\:{the}\:{answer}\:{of} \\ $$$$\mathrm{76808} \\ $$

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