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Question Number 35225 Answers: 0 Comments: 4

1) find f(a) = ∫_0 ^(2π) (dt/(a cos^2 t + sin^2 t)) with a≠0 2) find g(a) = ∫_0 ^(2π) ((cos^2 t)/((a cos^2 t +sin^2 t)^2 ))dt

$$\left.\mathrm{1}\right)\:{find}\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\:\frac{{dt}}{{a}\:{cos}^{\mathrm{2}} {t}\:+\:{sin}^{\mathrm{2}} {t}}\:{with}\:{a}\neq\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}^{\mathrm{2}} {t}}{\left({a}\:{cos}^{\mathrm{2}} {t}\:+{sin}^{\mathrm{2}} {t}\right)^{\mathrm{2}} }{dt}\: \\ $$

Question Number 35224 Answers: 1 Comments: 0

calculate ∫_0 ^(2π) ((1+2cost)/(5+4cost))dt

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\frac{\mathrm{1}+\mathrm{2}{cost}}{\mathrm{5}+\mathrm{4}{cost}}{dt} \\ $$

Question Number 35223 Answers: 1 Comments: 0

what is the value of cos(i+j) with i^2 =−1 and j =e^(i((2π)/3)) ?

$${what}\:{is}\:{the}\:{value}\:{of}\:{cos}\left({i}+{j}\right)\:{with}\:{i}^{\mathrm{2}} =−\mathrm{1}\:{and} \\ $$$${j}\:={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:\:? \\ $$

Question Number 35222 Answers: 1 Comments: 1

let ∣x∣<1 prove that arctanx =(i/2)ln(((i+x)/(i−x)))

$${let}\:\mid{x}\mid<\mathrm{1}\:{prove}\:{that}\: \\ $$$${arctanx}\:=\frac{{i}}{\mathrm{2}}{ln}\left(\frac{{i}+{x}}{{i}−{x}}\right) \\ $$

Question Number 35221 Answers: 0 Comments: 0

let z from C prove that e^z = Σ_(n=0) ^∞ (z^n /(n!)) .

$${let}\:{z}\:{from}\:{C}\:{prove}\:{that} \\ $$$${e}^{{z}} \:=\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{z}^{{n}} }{{n}!}\:. \\ $$

Question Number 35220 Answers: 0 Comments: 1

let z from C and f(z)= ((2z)/((z−1)(2z +1))) developp f at integr serie.

$${let}\:{z}\:{from}\:{C}\:{and}\:{f}\left({z}\right)=\:\frac{\mathrm{2}{z}}{\left({z}−\mathrm{1}\right)\left(\mathrm{2}{z}\:+\mathrm{1}\right)} \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 35219 Answers: 0 Comments: 0

let z ∈C prove that cosz =ch(iz) and sinz=sh(iz)

$${let}\:{z}\:\in{C}\:\:{prove}\:{that} \\ $$$${cosz}\:={ch}\left({iz}\right)\:{and}\:{sinz}={sh}\left({iz}\right) \\ $$

Question Number 35218 Answers: 0 Comments: 0

prove that ∫_0 ^∞ (t^(a−1) /(1+t))dt =(π/(sin(πa))) that we know 0<a<1 .

$${prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}{dt}\:=\frac{\pi}{{sin}\left(\pi{a}\right)} \\ $$$${that}\:{we}\:{know}\:\mathrm{0}<{a}<\mathrm{1}\:. \\ $$

Question Number 35217 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((x sin(2x))/(x^2 +4))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}\:{sin}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$

Question Number 35216 Answers: 0 Comments: 0

study the function f_n (x)=arcos(ncosx) n≥1 integr.

$${study}\:{the}\:{function}\: \\ $$$${f}_{{n}} \left({x}\right)={arcos}\left({ncosx}\right)\:{n}\geqslant\mathrm{1}\:{integr}. \\ $$

Question Number 35215 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^(+∞) ((cosx +cos(2x))/(x^2 +9))dx

$${find}\:{the}\:{value}\:{of}\:\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cosx}\:+{cos}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx} \\ $$

Question Number 35214 Answers: 0 Comments: 0

let a>0 b ∈C and Re(b)>0 cslculate ∫_(−∞) ^(+∞) (e^(iax) /(x−ib))dx and ∫_(−∞) ^(+∞) (e^(iax) /(x+ib))dx

$${let}\:{a}>\mathrm{0}\:\:{b}\:\in{C}\:{and}\:{Re}\left({b}\right)>\mathrm{0} \\ $$$${cslculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{e}^{{iax}} }{{x}−{ib}}{dx}\:\:{and}\:\int_{−\infty} ^{+\infty} \:\:\frac{{e}^{{iax}} }{{x}+{ib}}{dx} \\ $$

Question Number 35213 Answers: 0 Comments: 0

find the values of ∫_0 ^∞ cos(λx^2 )dx and ∫_0 ^∞ sin(λx^2 )dx with λ>0 . 2) find the values of ∫_0 ^∞ cos(x^2 )dx and ∫_0 ^∞ sin(x^2 )dx( integrals of fresnel)

$${find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left(\lambda{x}^{\mathrm{2}} \right){dx}\:{and} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:{sin}\left(\lambda{x}^{\mathrm{2}} \right){dx}\:{with}\:\lambda>\mathrm{0}\:. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}\:{and}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{\mathrm{2}} \right){dx}\left(\:{integrals}\:{of}\:{fresnel}\right) \\ $$

Question Number 35212 Answers: 0 Comments: 0

prove by using series only that ∫_0 ^∞ cos(x^2 )dx= ∫_0 ^∞ sin(x^2 )dx.

$${prove}\:{by}\:{using}\:{series}\:{only}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}=\:\int_{\mathrm{0}} ^{\infty} {sin}\left({x}^{\mathrm{2}} \right){dx}. \\ $$

Question Number 35208 Answers: 1 Comments: 0

The points A,B,C have coordinates (3,1),(1,5),(5,7) a) find the line l_1 joining the points A and B b)Find the line l_2 perpendicular to l_1 and passes through the point B c) show that the point C lie on the line l_(2 ) hence or otherwise find the area of the triangle ABC.

$${The}\:{points}\:{A},{B},{C}\:{have}\:{coordinates} \\ $$$$\left(\mathrm{3},\mathrm{1}\right),\left(\mathrm{1},\mathrm{5}\right),\left(\mathrm{5},\mathrm{7}\right) \\ $$$$\left.{a}\right)\:{find}\:{the}\:{line}\:{l}_{\mathrm{1}} \:{joining}\:{the}\:{points} \\ $$$${A}\:{and}\:{B} \\ $$$$\left.{b}\right){Find}\:{the}\:{line}\:{l}_{\mathrm{2}} \:{perpendicular} \\ $$$${to}\:{l}_{\mathrm{1}} \:{and}\:{passes}\:{through}\:{the}\:{point} \\ $$$${B} \\ $$$$\left.{c}\right)\:{show}\:{that}\:{the}\:{point}\:{C}\:{lie}\:{on}\:{the} \\ $$$${line}\:{l}_{\mathrm{2}\:\:} {hence}\:{or}\:{otherwise}\:{find}\: \\ $$$${the}\:{area}\:{of}\:{the}\:{triangle}\:{ABC}. \\ $$

Question Number 35202 Answers: 1 Comments: 0

∫^ e^(3x) (√(1−e^(2x) ))dx plzz help

$$\:\int^{} \:\boldsymbol{{e}}^{\mathrm{3}\boldsymbol{{x}}} \sqrt{\mathrm{1}−\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{{x}}} }\boldsymbol{{dx}} \\ $$$$\boldsymbol{{plzz}}\:\boldsymbol{{help}} \\ $$

Question Number 35197 Answers: 1 Comments: 0

Question Number 35195 Answers: 1 Comments: 1

Question Number 35258 Answers: 1 Comments: 0

Question Number 35186 Answers: 0 Comments: 0

find ∫_0 ^π ((x dx)/(3 +cosx))

$${find}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{x}\:{dx}}{\mathrm{3}\:+{cosx}} \\ $$

Question Number 35178 Answers: 0 Comments: 1

Question Number 35174 Answers: 1 Comments: 1

Question Number 35172 Answers: 0 Comments: 4

please I need android app that edit math equations in ARABIC

$$\mathrm{please} \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{android}\:\mathrm{app}\:\mathrm{that} \\ $$$$\mathrm{edit}\:\mathrm{math}\:\mathrm{equations} \\ $$$$\mathrm{in}\:\mathrm{ARABIC} \\ $$

Question Number 35167 Answers: 0 Comments: 2

Question Number 35165 Answers: 0 Comments: 2

In how many ways can a committee of 11 people be selected from 9 people.

$${In}\:{how}\:{many}\:{ways}\:{can}\:{a}\:{committee} \\ $$$${of}\:\mathrm{11}\:{people}\:{be}\:{selected}\:{from}\:\mathrm{9} \\ $$$${people}. \\ $$

Question Number 35153 Answers: 1 Comments: 0

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