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Question Number 42631 Answers: 1 Comments: 7

let f(x)=2(√(x−1)) −2x 1) find D_f 2) study the variation of f(x) 3 ) calculate ∫_1 ^3 f(x)dx 4) determine f^(−1) (x) and calculate ∫_1 ^3 f^(−1) (x)dx 5) find the values of A = ∫_1 ^3 ((f(x))/(f^(−1) (x)dx)) and B = ((∫_1 ^3 f(x))/(∫_1 ^3 f^(−1) (x))) dx.

$${let}\:{f}\left({x}\right)=\mathrm{2}\sqrt{{x}−\mathrm{1}}\:−\mathrm{2}{x} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{variation}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\:\right)\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:{f}\left({x}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{determine}\:{f}^{−\mathrm{1}} \left({x}\right)\:{and}\:{calculate}\:\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$$\left.\mathrm{5}\right)\:\:{find}\:{the}\:{values}\:{of}\:\:{A}\:=\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\:\:\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right){dx}}\:{and}\: \\ $$$${B}\:=\:\frac{\int_{\mathrm{1}} ^{\mathrm{3}} \:\:{f}\left({x}\right)}{\int_{\mathrm{1}} ^{\mathrm{3}} \:{f}^{−\mathrm{1}} \left({x}\right)}\:{dx}. \\ $$

Question Number 42630 Answers: 0 Comments: 0

let f(x) = e^x −2(√(x−3)) 1) find f^(−1) (x) 2) find ∫ f^(−1) (t)dt

$${let}\:{f}\left({x}\right)\:=\:{e}^{{x}} −\mathrm{2}\sqrt{{x}−\mathrm{3}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int\:\:{f}^{−\mathrm{1}} \left({t}\right){dt}\: \\ $$

Question Number 42629 Answers: 0 Comments: 0

find A_n =∫_0 ^∞ ((sin(nx))/(sh(2nx)))dx with n natural integr not 0.

$${find}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({nx}\right)}{{sh}\left(\mathrm{2}{nx}\right)}{dx}\:\:{with}\:{n}\:{natural}\:{integr} \\ $$$${not}\:\mathrm{0}. \\ $$

Question Number 42628 Answers: 0 Comments: 2

calculate I = ∫_(π/3) ^(π/2) ((cos(2x))/(sin(x)+cosx))dx and J =∫_(π/3) ^(π/2) ((sin(2x))/(sin(x) +cos(x)))dx

$${calculate}\:\:{I}\:\:=\:\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{{sin}\left({x}\right)+{cosx}}{dx}\:{and} \\ $$$${J}\:=\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{{sin}\left({x}\right)\:+{cos}\left({x}\right)}{dx} \\ $$

Question Number 42627 Answers: 2 Comments: 0

solve for x (1/3)log(x−3)+log5−log(x−2)^2 =0

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{\mathrm{log}}\left(\boldsymbol{{x}}−\mathrm{3}\right)+\boldsymbol{\mathrm{log}}\mathrm{5}−\boldsymbol{\mathrm{log}}\left(\boldsymbol{{x}}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 42624 Answers: 1 Comments: 2

Question Number 42622 Answers: 0 Comments: 1

find ∫ th(2x+1)dx

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

Question Number 42621 Answers: 0 Comments: 1

find ∫ th(x)dx

$${find}\:\int\:{th}\left({x}\right){dx}\: \\ $$

Question Number 42605 Answers: 0 Comments: 3

let f(x) = ∫_(−∞) ^(+∞) ((arctan (xt^2 ))/(1+2t^2 ))dt 1) find a explicite form of f(x) 2) calculate ∫_0 ^∞ ((arctan(t^2 ))/(1+2t^2 ))dt and ∫_0 ^∞ ((arctan(2t^2 ))/(1+2t^2 ))dt

$${let}\:{f}\left({x}\right)\:=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{arctan}\:\left({xt}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicite}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left({t}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} }{dt}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left(\mathrm{2}{t}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} }{dt} \\ $$$$ \\ $$

Question Number 42603 Answers: 0 Comments: 2

let f(x) =∫_0 ^1 ln(1+ixt)dt calculate f^, (x) (x from R).

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{ixt}\right){dt}\:\:{calculate}\:{f}^{,} \left({x}\right)\:\:\:\:\left({x}\:{from}\:{R}\right). \\ $$

Question Number 42593 Answers: 1 Comments: 1