Question and Answers Forum

AllQuestion and Answers: Page 1456

Question Number 65771 Answers: 0 Comments: 0

let X_n =∫_0 ^(π/4) sin^n xdx 1) calculate X_0 ,X_1 ,X_2 ,X_3 2) find X_n interms of n 3)find the value of ∫_0 ^(π/4) sin^8 xdx

$${let}\:{X}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{X}_{\mathrm{0}} \:,{X}_{\mathrm{1}} \:,{X}_{\mathrm{2}} ,{X}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{X}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{\mathrm{8}} {xdx} \\ $$

Question Number 65770 Answers: 0 Comments: 2

let A_n =∫_0 ^(π/2) cos^n xdx 1) calculate A_0 ,A_2 and A_3 2)calculate A_n interms of n 3) find ∫_0 ^(π/2) cos^8 xdx

$${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{0}} ,{A}_{\mathrm{2}} \:{and}\:{A}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{A}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{\mathrm{8}} {xdx}\: \\ $$

Question Number 65769 Answers: 0 Comments: 3

find the value of ∫_0 ^∞ (dx/((x^2 −2xcosθ +1)^2 ))

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{2}{xcos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 65768 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ (dx/(x^2 −2(cosθ)x +1))

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{2}\left({cos}\theta\right){x}\:+\mathrm{1}} \\ $$

Question Number 65767 Answers: 0 Comments: 0

let f(x) =∫_0 ^(+∞) (dt/(t^4 +x^4 )) with x>0 1) determine a explicit form of f(x) 2) find also g(x) =∫_0 ^∞ (dt/((t^4 +x^4 )^2 )) 3)give f^((n)) (x) at form of integral 4) calculate ∫_0 ^∞ (dt/(t^4 +8)) and ∫_0 ^∞ (dt/((t^4 +8)^2 )) 5) calculate A_n =∫_0 ^∞ (dt/((t^4 +x^4 )^n )) with n integr natural

$${let}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{4}} +{x}^{\mathrm{4}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{4}} \:+{x}^{\mathrm{4}} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{{t}^{\mathrm{4}} \:+\mathrm{8}}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{4}} \:+\mathrm{8}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{5}\right)\:{calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{4}} \:+{x}^{\mathrm{4}} \right)^{{n}} }\:\:{with}\:{n}\:{integr}\:{natural} \\ $$

Question Number 65763 Answers: 0 Comments: 0