Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1711

Question Number 36459 Answers: 2 Comments: 0

∫ e^(tan θ) (sec θ −sin θ) dθ = ?

$$\int\:\mathrm{e}^{\mathrm{tan}\:\theta} \left(\mathrm{sec}\:\theta\:−\mathrm{sin}\:\theta\right)\:\mathrm{d}\theta\:=\:? \\ $$

Question Number 36450 Answers: 1 Comments: 2

Question Number 36444 Answers: 0 Comments: 11

∫ (dx/((2x−7)(√((x−3)(x−4))))) = ?

$$\int\:\frac{\mathrm{d}{x}}{\left(\mathrm{2}{x}−\mathrm{7}\right)\sqrt{\left({x}−\mathrm{3}\right)\left({x}−\mathrm{4}\right)}}\:=\:? \\ $$

Question Number 36442 Answers: 0 Comments: 6

let f(x)= (√(2+x^2 )) −x 1) calculate lim_(x→+∞) f(x) and lim_(x→−∞) f(x) 2) calculate lim_(x→+∞) ((f(x))/x) and lim_(x→−∞) ((f(x))/x) 3) calculate f^′ (x) and determine its sign 4) give the variation of 5) give the equation of assymptote at point A(1,f(1)) 6) find f^(−1) (x) and calculate (f^(−1) )^′ (x) 7) calculate ∫_0 ^4 f(x)dx .

$${let}\:{f}\left({x}\right)=\:\sqrt{\mathrm{2}+{x}^{\mathrm{2}} \:}\:\:\:−{x} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow−\infty} {f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \:\frac{{f}\left({x}\right)}{{x}}\:{and}\:\:{lim}_{{x}\rightarrow−\infty} \:\frac{{f}\left({x}\right)}{{x}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{f}^{'} \left({x}\right)\:{and}\:{determine}\:{its}\:{sign} \\ $$$$\left.\mathrm{4}\right)\:{give}\:{the}\:{variation}\:{of} \\ $$$$\left.\mathrm{5}\right)\:{give}\:{the}\:{equation}\:{of}\:{assymptote}\:{at}\:\:{point} \\ $$$${A}\left(\mathrm{1},{f}\left(\mathrm{1}\right)\right) \\ $$$$\left.\mathrm{6}\right)\:{find}\:{f}^{−\mathrm{1}} \left({x}\right)\:{and}\:{calculate}\:\left({f}^{−\mathrm{1}} \right)^{'} \left({x}\right) \\ $$$$\left.\mathrm{7}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{4}} {f}\left({x}\right){dx}\:. \\ $$

Question Number 36441 Answers: 1 Comments: 1

find ∫ (e^(tanx) /(cos^2 x))dx

$${find}\:\:\int\:\:\:\frac{{e}^{{tanx}} }{{cos}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 36440 Answers: 0 Comments: 0

find ∫ (dx/((3+x^2 )^(1/3) ))

$${find}\:\int\:\:\:\:\frac{{dx}}{\left(\mathrm{3}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} } \\ $$

Question Number 36439 Answers: 1 Comments: 1

calculate ∫_0 ^π ((sin(2x))/(2 +cosx))dx

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{2}\:+{cosx}}{dx} \\ $$

Question Number 36438 Answers: 1 Comments: 3

let F(x) =∫_x ^(1/x) ((arctan(t))/t)dt 1) calculate (dF/dx)(x) 2) find F(x).

$${let}\:{F}\left({x}\right)\:=\int_{{x}} ^{\frac{\mathrm{1}}{{x}}} \:\:\frac{{arctan}\left({t}\right)}{{t}}{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:\frac{{dF}}{{dx}}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{F}\left({x}\right). \\ $$

Question Number 36437 Answers: 0 Comments: 3

simplify Σ_(k=0) ^n (C_n ^k /(k+1))

$${simplify}\:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\:\:\frac{{C}_{{n}} ^{{k}} }{{k}+\mathrm{1}} \\ $$

Question Number 36436 Answers: 2 Comments: 0

find ∫ ((sinx)/(1+cos^3 x))dx

$${find}\:\:\int\:\:\:\:\:\frac{{sinx}}{\mathrm{1}+{cos}^{\mathrm{3}} {x}}{dx} \\ $$

Question Number 36435 Answers: 0 Comments: 4

find the value of h(t)=∫_0 ^1 ln(1+tx^2 ) with ∣t∣≤1 2) calculate ∫_0 ^1 ln(1+x^2 )dx 3) calculate ∫_0 ^1 ln(1−x^2 )dx

$${find}\:{the}\:{value}\:{of}\:{h}\left({t}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{tx}^{\mathrm{2}} \right)\:\:{with}\:\mid{t}\mid\leqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 36434 Answers: 1 Comments: 1

find g(x) =∫_0 ^x (e^(−t) /(√(1+t^2 )))dt.

$${find}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{{x}} \:\:\:\frac{{e}^{−{t}} }{\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}{dt}. \\ $$

Question Number 36433 Answers: 2 Comments: 1

valculate f(x)= ∫_0 ^2 (((x+2)^2 )/(√(x^2 +4x+5)))dx

$${valculate}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{2}} \:\:\frac{\left({x}+\mathrm{2}\right)^{\mathrm{2}} }{\sqrt{{x}^{\mathrm{2}} \:+\mathrm{4}{x}+\mathrm{5}}}{dx} \\ $$

Question Number 36432 Answers: 1 Comments: 1

calculate I = ∫_(−∞) ^(+∞) ((x+1)/((x^2 +1)^2 ))dx .

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

Question Number 36431 Answers: 0 Comments: 1

calculate ∫_0 ^1 ((x+1)/((x^2 +1)^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 36430 Answers: 1 Comments: 1

find ∫ ((ln(x+x^2 ))/x^2 )dx

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

Question Number 36429 Answers: 1 Comments: 1

let ϕ(λ) = ∫_(λ/π) ^(π/λ) (1+(1/x^2 ))arctan(x)dx with λ>0 1) find a simple form of ϕ(λ) 2) calculate ϕ^′ (λ).

$${let}\:\:\varphi\left(\lambda\right)\:=\:\int_{\frac{\lambda}{\pi}} ^{\frac{\pi}{\lambda}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctan}\left({x}\right){dx}\:{with}\:\lambda>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:\varphi\left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\varphi^{'} \left(\lambda\right). \\ $$

Question Number 36428 Answers: 2 Comments: 1

find ∫ (dx/(cos^4 x +sin^4 x))

$${find}\:\:\int\:\:\:\:\frac{{dx}}{{cos}^{\mathrm{4}} {x}\:+{sin}^{\mathrm{4}} {x}} \\ $$

Question Number 36427 Answers: 1 Comments: 1

calculate ∫_(π/8) ^(π/6) (dx/(sin(2x)))

$${calculate}\:\int_{\frac{\pi}{\mathrm{8}}} ^{\frac{\pi}{\mathrm{6}}} \:\:\:\frac{{dx}}{{sin}\left(\mathrm{2}{x}\right)} \\ $$

Question Number 36426 Answers: 1 Comments: 0

find ∫ x^2 (√(1+x^3 )) dx

$${find}\:\:\int\:{x}^{\mathrm{2}} \sqrt{\mathrm{1}+{x}^{\mathrm{3}} \:}\:{dx} \\ $$

Question Number 36425 Answers: 2 Comments: 2

calculate ∫_1 ^4 ((x(√x))/(x^2 −5x +4))dx

$${calculate}\:\int_{\mathrm{1}} ^{\mathrm{4}} \:\:\:\frac{{x}\sqrt{{x}}}{{x}^{\mathrm{2}} \:−\mathrm{5}{x}\:+\mathrm{4}}{dx} \\ $$

Question Number 36424 Answers: 0 Comments: 2

find ∫ x^2 (√(x^2 −1))dx

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

Question Number 36423 Answers: 0 Comments: 0

find ∫ (dt/(t(√(t^2 +t+1))))

$${find}\:\int\:\:\:\:\:\frac{{dt}}{{t}\sqrt{{t}^{\mathrm{2}} \:+{t}+\mathrm{1}}} \\ $$

Question Number 36422 Answers: 0 Comments: 1

find f(x)= ∫_0 ^x (t^2 +1)arctan(t)dt .

$${find}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \left({t}^{\mathrm{2}} +\mathrm{1}\right){arctan}\left({t}\right){dt}\:. \\ $$

Question Number 36421 Answers: 0 Comments: 1

find ∫ (dx/(1+2(√(1−x))))

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

Question Number 36420 Answers: 0 Comments: 0

let f(x)=∫_0 ^∞ (( arctan(xt^2 ))/(1+t^4 ))dt 1) calculate f^′ (x) 2) find a simple form of f(x).

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\:{arctan}\left({xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right). \\ $$

Pg 1706 Pg 1707 Pg 1708 Pg 1709 Pg 1710 Pg 1711 Pg 1712 Pg 1713 Pg 1714 Pg 1715

Terms of Service

Contact: info@tinkutara.com