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IntegrationQuestion and Answers: Page 269

Question Number 43676 Answers: 0 Comments: 2

1)calculate I = ∫_0 ^∞ (dx/(x^2 −i)) and J = ∫_0 ^∞ (dx/(x^2 +i)) 2) find the value of ∫_0 ^∞ (dx/(x^4 +1))

$$\left.\mathrm{1}\right){calculate}\:\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}}\:\:{and}\:\:{J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+{i}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}} \\ $$

Question Number 43675 Answers: 0 Comments: 1

calculate ∫_1 ^2 (dx/(1+x^4 )) .

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

Question Number 43657 Answers: 3 Comments: 1

Question Number 43623 Answers: 1 Comments: 3

let f(x)=∫_0 ^x (dt/(1+t^4 )) 1) find a explicit form of f(x) 2) calculate ∫_0 ^∞ (dt/(1+t^4 ))

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$

Question Number 43551 Answers: 1 Comments: 0

evaluate ∫(1/(cos (x−a)cos (x−b)))dx

$${evaluate}\:\int\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}−{a}\right)\mathrm{cos}\:\left({x}−{b}\right)}{dx} \\ $$

Question Number 43550 Answers: 0 Comments: 1

prove that ∫_ 4_( ) ^4^4^x .4^4^x .4^x dx=(4^4^x /((log 4_e )))

$${prove}\:{that} \\ $$$$\int_{\:} \:\mathrm{4}_{\:\:\:\:\:} ^{\mathrm{4}^{\mathrm{4}^{{x}} } } .\mathrm{4}^{\mathrm{4}^{{x}} } .\mathrm{4}^{{x}} {dx}=\frac{\mathrm{4}^{\mathrm{4}^{{x}} } }{\left(\mathrm{log}\:\underset{{e}} {\mathrm{4}}\right)} \\ $$

Question Number 43539 Answers: 0 Comments: 1

calculate ∫∫_(0≤x≤1 ,0≤y≤1) (x+2y)e^(2x−y) dxdy

$${calculate}\:\int\int_{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\mathrm{0}\leqslant{y}\leqslant\mathrm{1}} \:\:\left({x}+\mathrm{2}{y}\right){e}^{\mathrm{2}{x}−{y}} {dxdy} \\ $$

Question Number 43538 Answers: 0 Comments: 1

calculate ∫∫_((x^2 /a^2 ) +(y^2 /b^2 ) ≤1) (x^2 −y^2 )dxdy whit a>0 and b>0 .

$${calculate}\:\int\int_{\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:\leqslant\mathrm{1}} \left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right){dxdy}\:{whit} \\ $$$${a}>\mathrm{0}\:{and}\:{b}>\mathrm{0}\:. \\ $$

Question Number 43517 Answers: 0 Comments: 1

Question Number 43589 Answers: 1 Comments: 3

Question Number 43490 Answers: 1 Comments: 2

evaluate ∫(√(tan𝛉 dθ))

$$\boldsymbol{\mathrm{evaluate}} \\ $$$$\int\sqrt{\boldsymbol{\mathrm{tan}\theta}\:\boldsymbol{\mathrm{d}}\theta} \\ $$

Question Number 43419 Answers: 0 Comments: 2

Question Number 43418 Answers: 1 Comments: 0

Question Number 43417 Answers: 1 Comments: 2

Question Number 43398 Answers: 0 Comments: 0

Question Number 43386 Answers: 4 Comments: 4

Question Number 43365 Answers: 0 Comments: 0

Question Number 43354 Answers: 1 Comments: 0

A particle starts from rest with acceleration(30+6t) ms^(−2) at time t. Where will the particle come to rest again?

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{with}\:\mathrm{acceleration}\left(\mathrm{30}+\mathrm{6t}\right) \\ $$$$\mathrm{ms}^{−\mathrm{2}} \:\mathrm{at}\:\mathrm{time}\:\mathrm{t}.\:\mathrm{Where}\:\mathrm{will}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{come}\:\mathrm{to}\:\mathrm{rest} \\ $$$$\mathrm{again}? \\ $$

Question Number 43342 Answers: 1 Comments: 0

using the substitution u=x+2, evaluate ∫_1 ^2 ((x−1)/((x+2)^4 ))

$$\mathrm{using}\:\mathrm{the}\:\mathrm{substitution}\:\mathrm{u}=\mathrm{x}+\mathrm{2},\:\mathrm{evaluate}\:\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\mathrm{x}−\mathrm{1}}{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{4}} } \\ $$

Question Number 43337 Answers: 0 Comments: 3

let f(x) =∫_0 ^x (t/(1+sint))dt 1)find a explicit form of f(x) 2) calculate ∫_0 ^∞ (t/(1+sint)) dt

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

Question Number 43324 Answers: 1 Comments: 0

Question Number 43322 Answers: 1 Comments: 1

Question Number 43319 Answers: 1 Comments: 0

Question Number 43191 Answers: 1 Comments: 3

integrate by use a partial friction ∫((lnx)/((1+x)^2 ))

$${integrate}\:{by}\:{use}\:{a}\:{partial}\:{friction} \\ $$$$\int\frac{{lnx}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} } \\ $$

Question Number 43190 Answers: 1 Comments: 1

a point move in such away that its its distance from the x−axis is alwa yas(1/5) its distance from origin. find the equetion of its path.

$${a}\:{point}\:{move}\:{in}\:{such}\:{away}\:{that}\:{its}\: \\ $$$${its}\:{distance}\:{from}\:{the}\:{x}−{axis}\:{is}\:{alwa} \\ $$$${yas}\frac{\mathrm{1}}{\mathrm{5}}\:{its}\:{distance}\:{from}\:{origin}. \\ $$$${find}\:{the}\:{equetion}\:{of}\:{its}\:{path}. \\ $$

Question Number 43159 Answers: 1 Comments: 0

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