Question and Answers Forum

IntegrationQuestion and Answers: Page 158

Question Number 103343 Answers: 1 Comments: 0

∫_0 ^1 x^(−x) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−{x}} {dx} \\ $$

Question Number 103312 Answers: 4 Comments: 0

∫_0 ^∞ (1/((1+x^2 )^6 )) dx ?

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{6}} }\:{dx}\:? \\ $$

Question Number 103241 Answers: 0 Comments: 0

∫x^(−x) dx

$$\int{x}^{−{x}} {dx} \\ $$

Question Number 103220 Answers: 1 Comments: 0

∫_0 ^∞ (x^3 /(e^x +1))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} }{{e}^{{x}} +\mathrm{1}}{dx} \\ $$

Question Number 103198 Answers: 4 Comments: 1

∫_0 ^1 sin(logx)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {sin}\left({logx}\right){dx} \\ $$

Question Number 103196 Answers: 1 Comments: 0

∫_0 ^1 ((((1/2)−x) ln(1−x) dx)/(x^2 −x+1)) ?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}−{x}\right)\:\mathrm{ln}\left(\mathrm{1}−{x}\right)\:{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\:? \\ $$

Question Number 103154 Answers: 2 Comments: 0

∫_0 ^1 logxlog(1−x)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {logxlog}\left(\mathrm{1}−{x}\right){dx} \\ $$

Question Number 103089 Answers: 1 Comments: 0

solve: (sin^2 (x)−y)dx−tan(x)dy=0

$${solve}: \\ $$$$\left({sin}^{\mathrm{2}} \left({x}\right)−{y}\right){dx}−{tan}\left({x}\right){dy}=\mathrm{0} \\ $$

Question Number 103080 Answers: 0 Comments: 0

calculate A_n =∫_0 ^∞ ((cos(nx))/((1+x^2 )^n ))dx with n integr natural

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({nx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }{dx} \\ $$$${with}\:{n}\:{integr}\:{natural} \\ $$

Question Number 103078 Answers: 0 Comments: 0

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

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

Question Number 103077 Answers: 0 Comments: 0

find ∫_0 ^∞ ((x^2 cosx)/((x^2 +x+2)^2 ))dx

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

Question Number 103040 Answers: 5 Comments: 0

given 5x+12y = 60 min value of (√(x^2 +y^2 ))

$${given}\:\mathrm{5}{x}+\mathrm{12}{y}\:=\:\mathrm{60} \\ $$$${min}\:{value}\:{of}\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$

Question Number 102987 Answers: 2 Comments: 0

lim_(x→0) ((x^2 sin (x^(−4) ))/x) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} \:\mathrm{sin}\:\left({x}^{−\mathrm{4}} \right)}{{x}}\:?\: \\ $$

Question Number 102926 Answers: 3 Comments: 0

∫ (dθ/(2sin^2 θ−cos^2 θ)) ?

$$\:\int\:\frac{{d}\theta}{\mathrm{2}{sin}^{\mathrm{2}} \theta−{cos}^{\mathrm{2}} \theta}\:\:? \\ $$

Question Number 102922 Answers: 1 Comments: 1

∫ (dx/(x^3 +3x−5)) ?

$$\int\:\frac{{dx}}{{x}^{\mathrm{3}} +\mathrm{3}{x}−\mathrm{5}}\:\:? \\ $$

Question Number 103071 Answers: 0 Comments: 0

∫(e^x /((1+x^2 )^2 ))∙(x^3 −x^2 +x+1)dx

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

Question Number 102911 Answers: 2 Comments: 1

∫ ((sin(x))/x) dx

$$\int\:\frac{\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{x}}\:\:\mathrm{dx} \\ $$

Question Number 102905 Answers: 1 Comments: 0

I=2∫_0 ^(1/(√2)) ((sin^(−1) (x))/x) dx −∫_0 ^1 ((tan^(−1) (x))/x)dx

$${I}=\mathrm{2}\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}} {\int}}\:\frac{\mathrm{sin}^{−\mathrm{1}} \left({x}\right)}{{x}}\:{dx}\:−\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}{{x}}{dx} \\ $$

Question Number 102790 Answers: 1 Comments: 0

I=2∫_0 ^(1/(√2)) ((sin^(−1) (x))/x) dx −∫_0 ^1 ((tan^(−1) (x))/x) dx

Question Number 102894 Answers: 3 Comments: 0

∫ (√(x+(√(x+(√(x+(√(x+(√(x+...)))))))))) dx

$$\int\:\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+...}}}}}\:\mathrm{dx}\: \\ $$

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

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

Pg 153 Pg 154 Pg 155 Pg 156 Pg 157 Pg 158 Pg 159 Pg 160 Pg 161 Pg 162

Contact: info@tinkutara.com