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IntegrationQuestion and Answers: Page 247

Question Number 51812 Answers: 0 Comments: 4

Question Number 51733 Answers: 2 Comments: 3

Question Number 51680 Answers: 1 Comments: 2

Solve the equation: (1) z^3 + 1 − 10i = 0 (2) z^4 − i + 2 = 0

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}:\:\:\:\:\: \\ $$$$\:\left(\mathrm{1}\right)\:\:\:\:\:\mathrm{z}^{\mathrm{3}} \:+\:\mathrm{1}\:−\:\mathrm{10i}\:\:=\:\:\mathrm{0} \\ $$$$\:\left(\mathrm{2}\right)\:\:\:\:\:\mathrm{z}^{\mathrm{4}} \:−\:\mathrm{i}\:+\:\mathrm{2}\:\:=\:\:\mathrm{0} \\ $$

Question Number 51594 Answers: 0 Comments: 0

Question Number 51552 Answers: 0 Comments: 1

calculate ∫_0 ^(+∞) ((arctan(1+x^2 ))/(x^2 +4))dx

$${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{arctan}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$

Question Number 51551 Answers: 2 Comments: 2

find f(λ) = ∫_0 ^(π/4) (√(1+λtant))dt with λ>0 also calculate ∫_0 ^(π/4) ((tant)/(√(1+λtant)))dt.

$${find}\:{f}\left(\lambda\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \sqrt{\mathrm{1}+\lambda{tant}}{dt}\:\:\:{with}\:\lambda>\mathrm{0} \\ $$$${also}\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\sqrt{\mathrm{1}+\lambda{tant}}}{dt}. \\ $$

Question Number 51550 Answers: 1 Comments: 2

find ∫_0 ^1 (√(1+x^4 ))dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 51526 Answers: 1 Comments: 1

Question Number 51510 Answers: 1 Comments: 0

Question Number 51501 Answers: 1 Comments: 0

Question Number 51456 Answers: 1 Comments: 0

∫ (x^8 /(x^6 + 64)) dx

$$\int\:\:\:\frac{\mathrm{x}^{\mathrm{8}} }{\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{64}}\:\mathrm{dx} \\ $$

Question Number 51421 Answers: 2 Comments: 3

∫ ((tan^(−1) x)/x^2 ) dx

$$\int\:\:\frac{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}}{\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 51419 Answers: 1 Comments: 0

∫ ((√x)/(1 + (x)^(1/3) )) dx

$$\int\:\frac{\sqrt{\mathrm{x}}}{\mathrm{1}\:+\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:\mathrm{dx} \\ $$

Question Number 51394 Answers: 1 Comments: 0

∫ (1/(1 + (√(tan x)))) dx

$$\int\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\sqrt{\mathrm{tan}\:\mathrm{x}}}\:\:\mathrm{dx} \\ $$

Question Number 51353 Answers: 4 Comments: 1

Question Number 51324 Answers: 2 Comments: 0

calculate ∫_0 ^(+∞) (dx/(1+x^(2 ) +x^4 ))

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

Question Number 51215 Answers: 1 Comments: 0

∫_0 ^π e^((1+i)x) dx=...

$$\int_{\mathrm{0}} ^{\pi} {e}^{\left(\mathrm{1}+{i}\right){x}} {dx}=... \\ $$

Question Number 51188 Answers: 0 Comments: 0

find ∫ ((cos^2 x)/(cosx +2sinx))dx

$${find}\:\:\int\:\:\:\:\:\frac{{cos}^{\mathrm{2}} {x}}{{cosx}\:+\mathrm{2}{sinx}}{dx} \\ $$

Question Number 51186 Answers: 1 Comments: 1

calculate ∫_0 ^1 (([nx])/(2x+1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\left[{nx}\right]}{\mathrm{2}{x}+\mathrm{1}}{dx} \\ $$

Question Number 51122 Answers: 1 Comments: 1

∫ (dx/(tgx−(√(tgx))))=?

$$\int\:\:\:\:\frac{\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{tgx}}−\sqrt{\boldsymbol{\mathrm{tgx}}}}=? \\ $$

Question Number 52893 Answers: 1 Comments: 0

∫sin x×cos x dx

$$\int\mathrm{sin}\:{x}×\mathrm{cos}\:{x}\:{dx} \\ $$

Question Number 51047 Answers: 0 Comments: 5

Question Number 50811 Answers: 1 Comments: 2

Question Number 50689 Answers: 1 Comments: 0

If c is the line segement from (0, 0, 0) to (1, 2, 3) find ∫ x e^(yz) ds

$$\mathrm{If}\:\:\mathrm{c}\:\mathrm{is}\:\mathrm{the}\:\mathrm{line}\:\mathrm{segement}\:\mathrm{from}\:\:\left(\mathrm{0},\:\mathrm{0},\:\mathrm{0}\right)\:\mathrm{to}\:\left(\mathrm{1},\:\mathrm{2},\:\mathrm{3}\right) \\ $$$$\mathrm{find}\:\:\:\int\:\mathrm{x}\:\mathrm{e}^{\mathrm{yz}} \:\:\mathrm{ds} \\ $$

Question Number 50683 Answers: 0 Comments: 1

find f(λ) =∫_0 ^∞ ((arctan(λx))/(1+λx^2 ))dx with λ>0

$${find}\:{f}\left(\lambda\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\lambda{x}\right)}{\mathrm{1}+\lambda{x}^{\mathrm{2}} }{dx}\:\:{with}\:\lambda>\mathrm{0} \\ $$

Question Number 50659 Answers: 2 Comments: 4

∫_(0 ) ^( ∞) (dx/(4−x^2 )) = ?

$$\int_{\mathrm{0}\:} ^{\:\infty} \:\frac{{dx}}{\mathrm{4}−{x}^{\mathrm{2}} }\:=\:? \\ $$

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