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IntegrationQuestion and Answers: Page 150

Question Number 102698 Answers: 2 Comments: 0

Question Number 102690 Answers: 3 Comments: 0

(1)∫(1/(cos (√x))) dx (2) ∫ (1/(2+cot x)) dx (3) ∫ (1/(ln(cos x))) dx

$$\left(\mathrm{1}\right)\int\frac{\mathrm{1}}{\mathrm{cos}\:\sqrt{\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\left(\mathrm{2}\right)\:\int\:\frac{\mathrm{1}}{\mathrm{2}+\mathrm{cot}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$$$\left(\mathrm{3}\right)\:\int\:\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{cos}\:\mathrm{x}\right)}\:\mathrm{dx}\: \\ $$

Question Number 102606 Answers: 2 Comments: 1

what is the volume of region bounded by y =x^2 −2x and y=x that is rotated about y=4 ?

$${what}\:{is}\:{the}\:{volume}\:{of}\:{region} \\ $$$${bounded}\:{by}\:{y}\:={x}^{\mathrm{2}} −\mathrm{2}{x}\:{and} \\ $$$${y}={x}\:{that}\:{is}\:{rotated}\:{about} \\ $$$${y}=\mathrm{4}\:? \\ $$

Question Number 102470 Answers: 1 Comments: 0

∫(dx/(x^(10) +x^2 ))

$$\int\frac{{dx}}{{x}^{\mathrm{10}} +{x}^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 102462 Answers: 8 Comments: 0

Calculate ; J=∫(dx/(x(x^2 +x−1)^2 )) K=∫((x^3 +x−1)/((x^2 +2)^2 ))dx L=∫(dx/(x+(√(x^2 +1))))

$$\mathrm{Calculate}\:; \\ $$$$\mathrm{J}=\int\frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mathrm{K}=\int\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{x}−\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$$$\mathrm{L}=\int\frac{\mathrm{dx}}{\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$

Question Number 102555 Answers: 0 Comments: 0

∫_0 ^1 ((x^(98) −99x+98)/(logx))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{98}} −\mathrm{99}{x}+\mathrm{98}}{{logx}}{dx} \\ $$

Question Number 102417 Answers: 3 Comments: 0

calculate ∫_0 ^∞ e^(−x) ln(1+e^x )dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$

Question Number 102416 Answers: 2 Comments: 0

calculate ∫_0 ^1 e^(−x) ln(1+e^x )dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{e}^{−\mathrm{x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$

Question Number 102397 Answers: 0 Comments: 0

∫ln(x−(√x)+1)dx

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

Question Number 102383 Answers: 0 Comments: 2

∫(x/(sin^2 x−3))

$$\int\frac{{x}}{{sin}^{\mathrm{2}} {x}−\mathrm{3}} \\ $$

Question Number 102381 Answers: 0 Comments: 0

∫((x(√6)sec^2 (x/2))/(1+9tan^4 (x/2)+18tan^2 (x/2)))dx

$$\int\frac{{x}\sqrt{\mathrm{6}}{sec}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{\mathrm{1}+\mathrm{9}{tan}^{\mathrm{4}} \frac{{x}}{\mathrm{2}}+\mathrm{18}{tan}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{dx} \\ $$

Question Number 102369 Answers: 3 Comments: 0

find the area bounded inner the curve r = 4−2cos θ and outer the curve r = 6+2cos θ

$${find}\:{the}\:{area}\:{bounded}\:{inner}\:{the}\:{curve} \\ $$$${r}\:=\:\mathrm{4}−\mathrm{2cos}\:\theta\:{and}\:{outer}\:{the}\:{curve}\:{r}\:=\:\mathrm{6}+\mathrm{2cos}\:\theta \\ $$

Question Number 102341 Answers: 4 Comments: 0

∫((xdx)/((1+x^2 )(√(1−x^2 ))))

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

Question Number 102366 Answers: 3 Comments: 0

∫_0 ^(π/2) ((cos x)/(1+cos x+sin x)) dx ?

$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}+\mathrm{sin}\:{x}}\:{dx}\:? \\ $$

Question Number 102303 Answers: 2 Comments: 1

∫ ((1+csc 2x)/(1−sin 2x)) dx ?

$$\int\:\frac{\mathrm{1}+\mathrm{csc}\:\mathrm{2}{x}}{\mathrm{1}−\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\:? \\ $$

Question Number 102330 Answers: 0 Comments: 0

Do this integration(please do it step by step and write the used formula) ∫(1/2)(sin x)(e^(sin x) )dx

$${Do}\:{this}\:{integration}\left({please}\:{do}\:{it}\:{step}\:{by}\:{step}\:{and}\:{write}\:{the}\:{used}\:{formula}\right) \\ $$$$\int\frac{\mathrm{1}}{\mathrm{2}}\left({sin}\:{x}\right)\left({e}^{{sin}\:{x}} \right){dx} \\ $$

Question Number 102275 Answers: 0 Comments: 2

∫_1 ^2 ln(((x^4 + 4)/(x^2 + 4)))(dx/x)

$$\int_{\mathrm{1}} ^{\mathrm{2}} \:\boldsymbol{{ln}}\left(\frac{\boldsymbol{{x}}^{\mathrm{4}} \:+\:\mathrm{4}}{\boldsymbol{{x}}^{\mathrm{2}} \:+\:\mathrm{4}}\right)\frac{\boldsymbol{{dx}}}{\boldsymbol{{x}}} \\ $$

Question Number 102233 Answers: 1 Comments: 0

Find the area under the curve y=(√(a^2 −x^2 )) included between the lines x=0 and x=4 plz help.....

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{under}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\sqrt{\mathrm{a}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{included}\:\mathrm{between}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{x}=\mathrm{0}\:\mathrm{and}\:\mathrm{x}=\mathrm{4} \\ $$$$ \\ $$$$\mathrm{plz}\:\mathrm{help}..... \\ $$

Question Number 102198 Answers: 2 Comments: 0

∫(x/(sin^2 x−3))dx=?

$$\int\frac{{x}}{{sin}^{\mathrm{2}} {x}−\mathrm{3}}{dx}=? \\ $$

Question Number 102195 Answers: 2 Comments: 0

∫sinx d(sinx)=?

$$\int{sinx}\:{d}\left({sinx}\right)=? \\ $$

Question Number 102169 Answers: 5 Comments: 0

∫_0 ^1 x^(3/2) (√(1−x)) dx ?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{\mathrm{3}/\mathrm{2}} \:\sqrt{\mathrm{1}−{x}}\:{dx}\:? \\ $$

Question Number 102165 Answers: 2 Comments: 0

calculate ∫_(−∞) ^∞ ((x^2 dx)/((x^2 −x+1)^3 ))

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

Question Number 102163 Answers: 1 Comments: 0

solve y^(′′) −2xy^′ =xe^(−x^2 )

$$\mathrm{solve}\:\:\mathrm{y}^{''} \:−\mathrm{2xy}^{'} \:\:=\mathrm{xe}^{−\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 102161 Answers: 0 Comments: 0

find ∫ ((x(√(x−1))−(x−1)(√x))/((x+1)(√x)−x(√(x+1)))) dx

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

Question Number 102160 Answers: 0 Comments: 0

1) let a<1 calculate ∫_0 ^π ((cosθdθ)/((a^2 −2acosθ +1)^2 )) 2) find the value of ∫_0 ^π ((cosθ)/((4−2(√3)cosθ)^2 ))dθ

$$\left.\mathrm{1}\right)\:\mathrm{let}\:\mathrm{a}<\mathrm{1}\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{cos}\theta\mathrm{d}\theta}{\left(\mathrm{a}^{\mathrm{2}} −\mathrm{2acos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{\mathrm{cos}\theta}{\left(\mathrm{4}−\mathrm{2}\sqrt{\mathrm{3}}\mathrm{cos}\theta\right)^{\mathrm{2}} }\mathrm{d}\theta \\ $$$$ \\ $$

Question Number 102158 Answers: 1 Comments: 0

calculate ∫_(−∞) ^(+∞) (dx/((x^2 +1)^2 (x^2 +9)^2 ))

$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{9}\right)^{\mathrm{2}} } \\ $$

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