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Question Number 200736 Answers: 0 Comments: 0

Solve: A particle moves along the space curve r_− =(t^2 +t)i+(3t−2)j+(2t^3 −4t^2 )k. find (a)velocity (b)speed or magnitude of velocity (c)acceleration (d)magnitude of acceleration at time t=2

$$\boldsymbol{{Solve}}:\:\boldsymbol{{A}}\:\boldsymbol{{particle}}\:\boldsymbol{{moves}}\:\boldsymbol{{along}}\:\boldsymbol{{the}}\:\boldsymbol{{space}} \\ $$$$\boldsymbol{{curve}}\:\underset{−} {\boldsymbol{{r}}}=\left(\boldsymbol{{t}}^{\mathrm{2}} +\boldsymbol{{t}}\right)\boldsymbol{{i}}+\left(\mathrm{3}\boldsymbol{{t}}−\mathrm{2}\right)\boldsymbol{{j}}+\left(\mathrm{2}\boldsymbol{{t}}^{\mathrm{3}} −\mathrm{4}\boldsymbol{{t}}^{\mathrm{2}} \right)\boldsymbol{{k}}. \\ $$$$\boldsymbol{{find}} \\ $$$$\left(\boldsymbol{{a}}\right)\boldsymbol{{velocity}} \\ $$$$\left(\boldsymbol{{b}}\right)\boldsymbol{{speed}}\:\boldsymbol{{or}}\:\boldsymbol{{magnitude}}\:\boldsymbol{{of}}\:\boldsymbol{{velocity}} \\ $$$$\left(\boldsymbol{{c}}\right)\boldsymbol{{acceleration}} \\ $$$$\left(\boldsymbol{{d}}\right)\boldsymbol{{magnitude}}\:\boldsymbol{{of}}\:\boldsymbol{{acceleration}}\:\boldsymbol{{at}}\:\boldsymbol{{time}}\:\boldsymbol{{t}}=\mathrm{2} \\ $$

Question Number 200697 Answers: 1 Comments: 0

Question Number 200685 Answers: 1 Comments: 0

∫_0 ^(π/4) ln (1+tanx)dx

$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\:\left(\mathrm{1}+\mathrm{tan}{x}\right){dx}\: \\ $$$$ \\ $$

Question Number 200684 Answers: 1 Comments: 0

∫_(−4π) ^(4π) ((∣x∣ sin^(2n) x)/(sin^(2n) x+cos^(2n) x))dx

$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{−\mathrm{4}\pi} ^{\mathrm{4}\pi} \:\:\:\frac{\mid{x}\mid\:\mathrm{sin}\:^{\mathrm{2}{n}} {x}}{\mathrm{sin}\:^{\mathrm{2}{n}} {x}+\mathrm{cos}\:^{\mathrm{2}{n}} {x}}{dx} \\ $$$$ \\ $$$$ \\ $$

Question Number 200606 Answers: 1 Comments: 0

Question Number 200605 Answers: 0 Comments: 4

Question Number 200604 Answers: 0 Comments: 2

Question Number 200603 Answers: 1 Comments: 0

Question Number 200602 Answers: 1 Comments: 0

Question Number 200601 Answers: 0 Comments: 6

Question Number 200586 Answers: 1 Comments: 0

Question Number 200570 Answers: 1 Comments: 0

Question Number 200569 Answers: 1 Comments: 0

Question Number 200553 Answers: 0 Comments: 0

∫_0 ^1 ((tan^(−1) (x))/( (√(1+x)))) dx =?

$$\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\:\sqrt{\mathrm{1}+\mathrm{x}}}\:\mathrm{dx}\:=?\: \\ $$

Question Number 200474 Answers: 1 Comments: 0

Question Number 200464 Answers: 1 Comments: 0

∫_0 ^(π/2) (dx/(1+tan^(2023) x))=???????

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\frac{{dx}}{\mathrm{1}+\mathrm{tan}^{\mathrm{2023}} \:{x}}=??????? \\ $$

Question Number 200444 Answers: 1 Comments: 0

Question Number 200403 Answers: 1 Comments: 0

∫ (((x^2 + 1)dx)/(x(x−1)(x+1))) = ??

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

Question Number 200366 Answers: 1 Comments: 1

Question Number 200257 Answers: 1 Comments: 0

Question Number 200256 Answers: 0 Comments: 0

Question Number 200254 Answers: 1 Comments: 0

calculate ... Ω = ∫_(∫_0 ^( (π/2)) ln(tan(x))dx) ^( ∫_0 ^( ∞) ((sin^2 (x))/x^2 ) dx) ln(sin(x))dx=?

$$ \\ $$$$\:\:\:\:\:\:{calculate}\:... \\ $$$$\:\:\Omega\:=\:\int_{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\left(\mathrm{tan}\left({x}\right)\right){dx}} ^{\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }\:{dx}} \mathrm{ln}\left(\mathrm{sin}\left({x}\right)\right){dx}=? \\ $$

Question Number 200253 Answers: 2 Comments: 0

Question Number 200250 Answers: 2 Comments: 0

Question Number 200159 Answers: 1 Comments: 2

Question Number 200155 Answers: 2 Comments: 0

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