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Question Number 95600 Answers: 1 Comments: 0

solve the differential equation L(d^2 q/dt^2 )+R(dq/dt)+(1/C)q=εcosωt which is in R.L.C circuit with forced oscillation where L is inductance R is resistance C is capacitanace q is charge ε is motion emf t is time

$${solve}\:{the}\:{differential}\:{equation} \\ $$$${L}\frac{{d}^{\mathrm{2}} {q}}{{dt}^{\mathrm{2}} }+{R}\frac{{dq}}{{dt}}+\frac{\mathrm{1}}{{C}}{q}=\varepsilon{cos}\omega{t} \\ $$$${which}\:{is}\:{in}\:{R}.{L}.{C}\:{circuit}\:{with}\:{forced}\:{oscillation} \\ $$$${where}\:{L}\:{is}\:{inductance} \\ $$$${R}\:{is}\:{resistance} \\ $$$${C}\:{is}\:{capacitanace} \\ $$$${q}\:{is}\:{charge} \\ $$$$\varepsilon\:{is}\:{motion}\:{emf} \\ $$$${t}\:{is}\:{time} \\ $$

Question Number 95598 Answers: 0 Comments: 0

If sin^(−1) x_1 +sin^(−1) x_2 +...+sin^(−1) x_(2n) =nπ, then Σ^(2n) _(i, j=1_(i ≠ j) ) x_i x_j =

$$\mathrm{If}\:\:\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{1}} +\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{2}} +...+\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{2}{n}} ={n}\pi, \\ $$$$\mathrm{then}\:\:\:\underset{\underset{{i}\:\neq\:{j}} {{i},\:{j}=\mathrm{1}}} {\overset{\mathrm{2}{n}} {\sum}}\:\:\:{x}_{{i}} \:{x}_{{j}} \:= \\ $$

Question Number 95597 Answers: 0 Comments: 1

The value of cosec^2 (π/7)+cosec^2 ((2π)/7)+cosec^2 ((3π)/7) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cosec}^{\mathrm{2}} \:\frac{\pi}{\mathrm{7}}+\mathrm{cosec}^{\mathrm{2}} \:\frac{\mathrm{2}\pi}{\mathrm{7}}+\mathrm{cosec}^{\mathrm{2}} \:\frac{\mathrm{3}\pi}{\mathrm{7}}\:\mathrm{is} \\ $$

Question Number 95593 Answers: 0 Comments: 2

if f(x) = ((sin x)/((1 + x^2 +x^6 )^2 )) is odd, find ∫_(−3) ^3 f(x) dx

$$\mathrm{if}\:{f}\left({x}\right)\:=\:\frac{\mathrm{sin}\:{x}}{\left(\mathrm{1}\:+\:{x}^{\mathrm{2}} \:+{x}^{\mathrm{6}} \right)^{\mathrm{2}} }\:\mathrm{is}\:\mathrm{odd}, \\ $$$$\mathrm{find}\:\underset{−\mathrm{3}} {\overset{\mathrm{3}} {\int}}{f}\left({x}\right)\:{dx} \\ $$

Question Number 95586 Answers: 1 Comments: 1

find ∫ (dx/(x^n (x+1)^m )) m and n integr

$${find}\:\int\:\:\frac{{dx}}{{x}^{{n}} \left({x}+\mathrm{1}\right)^{{m}} }\:\: \\ $$$${m}\:{and}\:{n}\:{integr} \\ $$

Question Number 95585 Answers: 1 Comments: 0

calculate ∫_2 ^(+∞) (dx/((x−1)^4 (x^2 +x+1)^2 ))

$${calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}−\mathrm{1}\right)^{\mathrm{4}} \left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 95584 Answers: 3 Comments: 0

calculate ∫_1 ^(+∞) (dx/(x^3 (2x+1)^4 )) 1)without use of decomposition 2)by use of decomposition

$${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{3}} \left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right){without}\:{use}\:{of}\:{decomposition} \\ $$$$\left.\mathrm{2}\right){by}\:{use}\:{of}\:{decomposition} \\ $$

Question Number 95581 Answers: 0 Comments: 0

∫ln∣cot(x/2)∣dx

$$\int\mathrm{ln}\mid\mathrm{cot}\left(\mathrm{x}/\mathrm{2}\right)\mid\mathrm{dx} \\ $$

Question Number 95578 Answers: 0 Comments: 8

Question Number 95563 Answers: 1 Comments: 0

∫((ax^2 +bx+c)/((x−p)(x−q)(x−r)))dx

$$\int\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\left(\mathrm{x}−\mathrm{p}\right)\left(\mathrm{x}−\mathrm{q}\right)\left(\mathrm{x}−\mathrm{r}\right)}\mathrm{dx} \\ $$

Question Number 95562 Answers: 1 Comments: 0

show that ∫((sin (x−θ))/(sin x))dx=xcos x−sin θlog sin x

$$\mathrm{show}\:\mathrm{that} \\ $$$$\int\frac{\mathrm{sin}\:\left(\mathrm{x}−\theta\right)}{\mathrm{sin}\:\mathrm{x}}\mathrm{dx}=\mathrm{xcos}\:\mathrm{x}−\mathrm{sin}\:\theta\mathrm{log}\:\mathrm{sin}\:\mathrm{x} \\ $$

Question Number 95560 Answers: 1 Comments: 1

Question Number 95557 Answers: 0 Comments: 0

Question Number 95549 Answers: 3 Comments: 0

∫_(−π) ^π ∣cos^3 x∣dx

$$\int_{−\pi} ^{\pi} \mid{cos}^{\mathrm{3}} {x}\mid{dx} \\ $$

Question Number 95548 Answers: 0 Comments: 2

Question Number 95547 Answers: 2 Comments: 0

∫((2x^3 dx)/(2x^2 −4x+3))=?

$$\int\frac{\mathrm{2}{x}^{\mathrm{3}} {dx}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}=? \\ $$

Question Number 95546 Answers: 2 Comments: 0

∫x^2 (√(a^2 +x^2 ))dx=?

$$\int{x}^{\mathrm{2}} \sqrt{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }{dx}=? \\ $$

Question Number 95531 Answers: 0 Comments: 4

((tanx×ctg2x)/(tan^2 x−1))=?

$$\frac{\mathrm{tanx}×\mathrm{ctg2x}}{\mathrm{tan}^{\mathrm{2}} \mathrm{x}−\mathrm{1}}=? \\ $$

Question Number 95524 Answers: 0 Comments: 4

(1/(sin10))−((√3)/(cos10))=?

$$\frac{\mathrm{1}}{\mathrm{sin10}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{cos10}}=? \\ $$

Question Number 95520 Answers: 0 Comments: 0

For 0<x<(π/(6 )), all the values of tan^2 (3x)cos^2 (x)−4tan (3x)sin (2x)+16sin^2 (x) lie in the interval (a). (0,((121)/(36))) (b).(1,((121)/9)) (c). (−1,0) (d). None of these.

$$\mathrm{For}\:\mathrm{0}<\mathrm{x}<\frac{\pi}{\mathrm{6}\:},\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of} \\ $$$$\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{3x}\right)\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{4tan}\:\left(\mathrm{3x}\right)\mathrm{sin}\:\left(\mathrm{2x}\right)+\mathrm{16sin}\:^{\mathrm{2}} \left(\mathrm{x}\right) \\ $$$$\mathrm{lie}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left(\mathrm{a}\right).\:\left(\mathrm{0},\frac{\mathrm{121}}{\mathrm{36}}\right)\:\left(\mathrm{b}\right).\left(\mathrm{1},\frac{\mathrm{121}}{\mathrm{9}}\right)\:\left(\mathrm{c}\right).\:\left(−\mathrm{1},\mathrm{0}\right)\:\left(\mathrm{d}\right).\:\mathrm{None}\:\mathrm{of}\:\mathrm{these}. \\ $$

Question Number 95518 Answers: 0 Comments: 0