Question and Answers Forum

IntegrationQuestion and Answers: Page 295

Question Number 32718 Answers: 0 Comments: 0

find ∫_0 ^∞ arctan(2x) (e^(−tx) /x) dc with t>0 2) calculate ∫_0 ^∞ ((arctan(2x))/x) e^(−x) dx.

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:{arctan}\left(\mathrm{2}{x}\right)\:\frac{{e}^{−{tx}} }{{x}}\:{dc}\:{with}\:{t}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{{x}}\:{e}^{−{x}} \:{dx}. \\ $$

Question Number 32717 Answers: 0 Comments: 0

finf ∫_0 ^(+∞) (dx/(1+x^2 +x^4 ))

$${finf}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} } \\ $$

Question Number 32716 Answers: 1 Comments: 0

find ∫_0 ^(2π) ((cos^2 x)/(1+3sin^2 x))dx .

$${find}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cos}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{3}{sin}^{\mathrm{2}} {x}}{dx}\:. \\ $$

Question Number 32715 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) (dt/((1+it)(1+it^2 ))) .

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dt}}{\left(\mathrm{1}+{it}\right)\left(\mathrm{1}+{it}^{\mathrm{2}} \right)}\:\:. \\ $$

Question Number 32714 Answers: 0 Comments: 1

calculate ∫_1 ^(+∞) (dt/(t^2 (√(1+t^2 )))) .

$${calculate}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{dt}}{{t}^{\mathrm{2}} \sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\:. \\ $$

Question Number 32712 Answers: 0 Comments: 1

calculate ∫_0 ^(π/2) (dt/(1+a cos^2 t)) .

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{dt}}{\mathrm{1}+{a}\:{cos}^{\mathrm{2}} {t}}\:. \\ $$

Question Number 32722 Answers: 0 Comments: 0

find ∫_0 ^∞ (dx/(1+x^3 )) .

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} }\:. \\ $$

Question Number 32705 Answers: 0 Comments: 1

let give f(x)= ∫_0 ^∞ ln(1 +(x/t^2 ))dt with ∣x∣<1 find a simple form of f(x).

$${let}\:{give}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:{ln}\left(\mathrm{1}\:+\frac{{x}}{{t}^{\mathrm{2}} }\right){dt}\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right). \\ $$

Question Number 32704 Answers: 0 Comments: 0

find ∫_0 ^∞ (((x+1)(√x))/(2+x^2 ))dx.

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left({x}+\mathrm{1}\right)\sqrt{{x}}}{\mathrm{2}+{x}^{\mathrm{2}} }{dx}. \\ $$

Question Number 32675 Answers: 1 Comments: 1

Question Number 32708 Answers: 0 Comments: 1

let give f(x)=∫_0 ^(π/2) ((ln(1+xtant))/(tant))dt find a simple form of f(x) 2)calculate ∫_0 ^(π/2) ((ln(1+2tant))/(tant))dt .

$${let}\:{give}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{ln}\left(\mathrm{1}+{xtant}\right)}{{tant}}{dt} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{ln}\left(\mathrm{1}+\mathrm{2}{tant}\right)}{{tant}}{dt}\:. \\ $$

Question Number 32627 Answers: 0 Comments: 1

plzz help ne differentiate between ∫sin(2x)= −(1/2)cox(2x)+c is not change to ∫2sin(x)cos(x) but ∫_b ^a sin(2x)= is change to ∫_b ^a 2sin(x)cos(x)

$${plzz}\:{help}\:{ne}\:{differentiate}\: \\ $$$${between} \\ $$$$\int{sin}\left(\mathrm{2}{x}\right)=\:−\frac{\mathrm{1}}{\mathrm{2}}{cox}\left(\mathrm{2}{x}\right)+{c}\: \\ $$$${is}\:{not}\:{change}\:{to}\:\int\mathrm{2}{sin}\left({x}\right){cos}\left({x}\right) \\ $$$${but}\:\underset{{b}} {\overset{{a}} {\int}}{sin}\left(\mathrm{2}{x}\right)=\:{is}\:{change}\:{to} \\ $$$$\underset{{b}} {\overset{{a}} {\int}}\mathrm{2}{sin}\left({x}\right){cos}\left({x}\right) \\ $$

Question Number 32484 Answers: 0 Comments: 2

∫_1 ^2 ∫_0 ^1 ((ln(x+y))/((x+y))) dx dy

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

Question Number 32483 Answers: 0 Comments: 2

calculate ∫_0 ^(2π) (dx/(1+2cosx)) .

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\frac{{dx}}{\mathrm{1}+\mathrm{2}{cosx}}\:. \\ $$

Question Number 32482 Answers: 0 Comments: 0

find f(x)= ∫_0 ^π ((sin^2 t)/(1−2xcost +x^2 ))dt with ∣x∣<1 .

$${find}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\frac{{sin}^{\mathrm{2}} {t}}{\mathrm{1}−\mathrm{2}{xcost}\:+{x}^{\mathrm{2}} }{dt}\:{with}\:\mid{x}\mid<\mathrm{1}\:. \\ $$

Question Number 32481 Answers: 0 Comments: 0

find ∫_0 ^∞ ((√(t )) −2(√(t+1)) +(√(t+2))) dt

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\left(\sqrt{{t}\:}\:−\mathrm{2}\sqrt{{t}+\mathrm{1}}\:+\sqrt{\left.{t}+\mathrm{2}\right)}\:{dt}\right. \\ $$

Question Number 32480 Answers: 0 Comments: 1

find ∫_0 ^α (√(tanx)) dx with 0<α<(π/2) .

$${find}\:\:\int_{\mathrm{0}} ^{\alpha} \:\sqrt{{tanx}}\:{dx}\:{with}\:\mathrm{0}<\alpha<\frac{\pi}{\mathrm{2}}\:. \\ $$

Question Number 32479 Answers: 0 Comments: 0

find ∫_0 ^∞ (dx/((x^2 +1)(x^2 +3x +1)))

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}{x}\:+\mathrm{1}\right)} \\ $$

Question Number 32478 Answers: 0 Comments: 1

find ∫_0 ^∞ ln(((1+t^2 )/t^2 ))dt

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:{ln}\left(\frac{\mathrm{1}+{t}^{\mathrm{2}} }{{t}^{\mathrm{2}} }\right){dt} \\ $$

Question Number 32477 Answers: 0 Comments: 1

calcilate ∫_0 ^1 ((ln(1−x^2 ))/x^2 )dx

$${calcilate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 32420 Answers: 0 Comments: 0

Question Number 32419 Answers: 0 Comments: 0

$$ \\ $$

Question Number 32367 Answers: 0 Comments: 0

let α∈R and x^2 ≠1 find the value of f(x) = ∫_0 ^π ln(x^2 −2x cost +1)dt calculate f(x).

$${let}\:\alpha\in{R}\:{and}\:{x}^{\mathrm{2}} \neq\mathrm{1}\:\:{find}\:{the}\:{value}\:{of} \\ $$$${f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left({x}^{\mathrm{2}} −\mathrm{2}{x}\:{cost}\:+\mathrm{1}\right){dt} \\ $$$${calculate}\:{f}\left({x}\right). \\ $$

Question Number 32365 Answers: 0 Comments: 3

let F(x) = ∫_0 ^π ln(1+xcosθ)dθ .with ∣x∣<1 find F(x) .

$${let}\:{F}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{1}+{xcos}\theta\right){d}\theta\:.{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${find}\:{F}\left({x}\right)\:. \\ $$

Question Number 32363 Answers: 0 Comments: 1

let consider the function f(x,θ) = ∫_x ^x^2 ln( 2+sinθ cost)dt calculate (∂f/∂x)(x,θ) and (∂f/∂θ)(x,θ) .

$${let}\:{consider}\:{the}\:{function} \\ $$$${f}\left({x},\theta\right)\:=\:\:\int_{{x}} ^{{x}^{\mathrm{2}} } {ln}\left(\:\mathrm{2}+{sin}\theta\:{cost}\right){dt} \\ $$$${calculate}\:\frac{\partial{f}}{\partial{x}}\left({x},\theta\right)\:{and}\:\:\frac{\partial{f}}{\partial\theta}\left({x},\theta\right)\:. \\ $$

Question Number 32362 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/((2x+1)(2x+3)(2x+5))) .

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{2}{x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{3}\right)\left(\mathrm{2}{x}+\mathrm{5}\right)}\:. \\ $$

Pg 290 Pg 291 Pg 292 Pg 293 Pg 294 Pg 295 Pg 296 Pg 297 Pg 298 Pg 299

Contact: info@tinkutara.com