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IntegrationQuestion and Answers: Page 187

Question Number 87543 Answers: 0 Comments: 0

Question Number 87540 Answers: 1 Comments: 1

Question Number 87538 Answers: 0 Comments: 7

Question Number 87534 Answers: 0 Comments: 1

calculate ∫_0 ^(π/4) ((arctan(sinx))/(sinx))dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{arctan}\left({sinx}\right)}{{sinx}}{dx} \\ $$

Question Number 87527 Answers: 0 Comments: 1

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

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

Question Number 87526 Answers: 0 Comments: 1

calculate ∫_0 ^∞ e^(−[nx]) dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left[{nx}\right]} \:{dx} \\ $$

Question Number 87511 Answers: 2 Comments: 0

Question Number 87503 Answers: 1 Comments: 4

∫(x^2 /(1+x^5 ))dx

$$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{5}} }{dx} \\ $$

Question Number 87854 Answers: 0 Comments: 3

∫ (1/(sin x+2cos x+3)) dx

$$\int\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}+\mathrm{2cos}\:\mathrm{x}+\mathrm{3}}\:\mathrm{dx} \\ $$

Question Number 87461 Answers: 1 Comments: 1

∫_e^(-1) ^e ((√(1−(lnx)^2 ))/x) dx

$$\underset{{e}^{-\mathrm{1}} } {\overset{\mathrm{e}} {\int}}\:\frac{\sqrt{\mathrm{1}−\left(\mathrm{ln}{x}\right)^{\mathrm{2}} }}{{x}}\:{dx} \\ $$

Question Number 87371 Answers: 1 Comments: 3

∫((x^7 +x^3 +4)/(x^8 −x^5 +9))dx

$$\int\frac{{x}^{\mathrm{7}} +{x}^{\mathrm{3}} +\mathrm{4}}{{x}^{\mathrm{8}} −{x}^{\mathrm{5}} +\mathrm{9}}{dx} \\ $$

Question Number 87340 Answers: 3 Comments: 3

∫ ((cos x)/((5+4cos x)^2 )) dx =

$$\int\:\frac{\mathrm{cos}\:\mathrm{x}}{\left(\mathrm{5}+\mathrm{4cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}\:= \\ $$

Question Number 87325 Answers: 1 Comments: 3

1) ∫e^(√x) dx 2)∫((√(sin(x)))/((√(sin(x)))+(√(cos(x)))))dx

$$\left.\mathrm{1}\right)\:\int{e}^{\sqrt{{x}}} \:{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{\sqrt{{sin}\left({x}\right)}}{\sqrt{{sin}\left({x}\right)}+\sqrt{{cos}\left({x}\right)}}{dx} \\ $$

Question Number 87306 Answers: 1 Comments: 9

calculate by complex method ∫_1 ^(+∞) ((xdx)/(x^4 +1))

$${calculate}\:{by}\:{complex}\:{method}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{xdx}}{{x}^{\mathrm{4}} \:+\mathrm{1}} \\ $$

Question Number 87301 Answers: 0 Comments: 3

Question Number 87298 Answers: 1 Comments: 0

If y=sin x , x=0 to x=2π is revolved about the x-axis, find the surface of the solid of revolution.

$${If}\:{y}=\mathrm{sin}\:{x}\:,\:\:{x}=\mathrm{0}\:{to}\:{x}=\mathrm{2}\pi\:{is} \\ $$$${revolved}\:{about}\:{the}\:{x}-{axis},\:{find} \\ $$$${the}\:{surface}\:{of}\:{the}\:{solid}\:{of} \\ $$$${revolution}. \\ $$

Question Number 87296 Answers: 1 Comments: 0

If ellipse (x^2 /a^2 )+(y^2 /b^2 )=1 (a>b) is rotated about x-axis, find the surface of the solid of revolution.

$${If}\:\:{ellipse}\:\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:\:\left({a}>{b}\right) \\ $$$${is}\:{rotated}\:{about}\:{x}-{axis},\:{find}\:{the} \\ $$$${surface}\:{of}\:{the}\:{solid}\:{of}\:{revolution}. \\ $$

Question Number 87279 Answers: 3 Comments: 2

∫(x^2 /(1+x^4 ))dx

$$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 87185 Answers: 3 Comments: 0

∫((2x−1)/(x(x^2 +3)))dx

$$\int\frac{\mathrm{2}{x}−\mathrm{1}}{{x}\left({x}^{\mathrm{2}} +\mathrm{3}\right)}{dx} \\ $$

Question Number 87121 Answers: 3 Comments: 0

∫_0 ^(π/2) ((1−x^4 )/(1+x^4 ))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}−{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 87103 Answers: 2 Comments: 2

∫(dx/((1+x)(√(x−x^2 ))))

$$\int\frac{{dx}}{\left(\mathrm{1}+{x}\right)\sqrt{{x}−{x}^{\mathrm{2}} }} \\ $$

Question Number 87086 Answers: 1 Comments: 0

Question Number 87052 Answers: 0 Comments: 4

f(x)=∫_0 ^(π/2) ((sin^2 (t))/(1+xsin^2 (t)))dt

$${f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{sin}^{\mathrm{2}} \left({t}\right)}{\mathrm{1}+{xsin}^{\mathrm{2}} \left({t}\right)}{dt} \\ $$

Question Number 87046 Answers: 1 Comments: 0

∫(dx/(sin^3 x+cos^3 x))

$$\int\frac{{dx}}{{sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}} \\ $$

Question Number 87048 Answers: 0 Comments: 0

Express into partial fractions (x^6 /(x^(12) +1))

$${Express}\:\:{into}\:\:{partial}\:\:{fractions} \\ $$$$\:\:\:\:\:\:\:\:\frac{{x}^{\mathrm{6}} }{{x}^{\mathrm{12}} +\mathrm{1}} \\ $$

Question Number 87025 Answers: 0 Comments: 2

∫_0 ^(π/2) ((arc tan ((√2) tan x))/(tan x)) dx?

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{arc}\:\mathrm{tan}\:\left(\sqrt{\mathrm{2}}\:\mathrm{tan}\:\mathrm{x}\right)}{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}?\: \\ $$

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