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IntegrationQuestion and Answers: Page 199

Question Number 83899 Answers: 0 Comments: 1

Defined a function f(x) such that f(1−x)+2f(x)= nx for m ,n > 1 , the value of ∫ _1 ^( m) (2n+6f((m/x))) dx is ...

$$\mathrm{Defined}\:\mathrm{a}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{such}\: \\ $$$$\mathrm{that}\:\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)+\mathrm{2f}\left(\mathrm{x}\right)=\:\mathrm{nx}\: \\ $$$$\mathrm{for}\:\mathrm{m}\:,\mathrm{n}\:>\:\mathrm{1}\:,\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\int\underset{\mathrm{1}} {\overset{\:\mathrm{m}} {\:}}\left(\mathrm{2n}+\mathrm{6f}\left(\frac{\mathrm{m}}{\mathrm{x}}\right)\right)\:\mathrm{dx}\:\mathrm{is}\:... \\ $$

Question Number 83898 Answers: 0 Comments: 4

∫(du/((√(u^2 −1 ))−u))

$$\int\frac{\mathrm{du}}{\sqrt{\mathrm{u}^{\mathrm{2}} −\mathrm{1}\:}−\mathrm{u}} \\ $$

Question Number 83893 Answers: 0 Comments: 1

∫(du/(u−u^2 ))

$$\int\frac{\mathrm{du}}{\mathrm{u}−\mathrm{u}^{\mathrm{2}} } \\ $$

Question Number 83852 Answers: 0 Comments: 3

f(α)=∫_0 ^∞ ((e^(−αx) sin(x))/x)dx

$${f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−\alpha{x}} {sin}\left({x}\right)}{{x}}{dx} \\ $$

Question Number 83842 Answers: 0 Comments: 4

∫((ln(x))/(ln(6x−x^2 )))dx

$$\int\frac{{ln}\left({x}\right)}{{ln}\left(\mathrm{6}{x}−{x}^{\mathrm{2}} \right)}{dx} \\ $$

Question Number 83819 Answers: 1 Comments: 0

If the function of f is continous in R and ∫ _0 ^( x) f(t)dt = ∫ _x ^( 1) t^2 f(t) dt + 2x^2 +4x+c , ∀x∈R. The value of constant c is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{function}\:\mathrm{of}\:\mathrm{f}\:\mathrm{is}\:\mathrm{continous} \\ $$$$\mathrm{in}\:\mathbb{R}\:\mathrm{and}\:\int\underset{\mathrm{0}} {\overset{\:\mathrm{x}} {\:}}\:\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt}\:=\:\int\underset{\mathrm{x}} {\overset{\:\mathrm{1}} {\:}}\mathrm{t}^{\mathrm{2}} \mathrm{f}\left(\mathrm{t}\right)\:\mathrm{dt}\:+\: \\ $$$$\mathrm{2x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{c}\:,\:\forall\mathrm{x}\in\mathbb{R}. \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{constant}\:\mathrm{c}\:\mathrm{is}\: \\ $$

Question Number 83807 Answers: 2 Comments: 1

Evaluate: ∫ (( 1)/(ax^2 +bx+c))dx

$$\:\:\boldsymbol{\mathrm{Evaluate}}: \\ $$$$\:\:\int\:\:\frac{\:\mathrm{1}}{\boldsymbol{\mathrm{ax}}^{\mathrm{2}} +\boldsymbol{\mathrm{bx}}+\boldsymbol{\mathrm{c}}}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 83805 Answers: 3 Comments: 1

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

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{sin}\left({x}\right)+{cos}\left({x}\right)}\:{dx} \\ $$

Question Number 83892 Answers: 0 Comments: 0

∫(du/(u−u^2 ))

$$\int\frac{\mathrm{du}}{\mathrm{u}−\mathrm{u}^{\mathrm{2}} } \\ $$

Question Number 83781 Answers: 1 Comments: 2

∫ _0^(π/2) (1/(4sin^2 x+5cos^2 x)) dx

$$\int\:_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{4sin}\:^{\mathrm{2}} {x}+\mathrm{5cos}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$

Question Number 83750 Answers: 0 Comments: 0

I=∫e^x tan(x) dx

$${I}=\int{e}^{{x}} \:{tan}\left({x}\right)\:{dx} \\ $$

Question Number 83737 Answers: 0 Comments: 0

∫ (x^3 /(x^4 +cos x)) dx ?

$$\int\:\:\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{4}} +\mathrm{cos}\:{x}}\:{dx}\:? \\ $$

Question Number 83713 Answers: 1 Comments: 8

∫(dx/(√(x+(√(x+(√x)))))) pleas sir help me

$$\int\frac{{dx}}{\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}\:\:\:{pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 83691 Answers: 1 Comments: 2

evaluate: ∫ (( dx)/(a sin x+b cos x))

$$\:\mathrm{evaluate}: \\ $$$$\:\:\:\int\:\frac{\:\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{b}}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}} \\ $$

Question Number 83675 Answers: 1 Comments: 2

evaluate: 2 ∫_0 ^( 2) ((√(x+1))/(x^2 +4))dx

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

Question Number 83642 Answers: 0 Comments: 0

Find the surface area of the solid generated by the revolution of the cardioids r=a(1+cos θ) about the initial line.

$$ \\ $$$$\: \\ $$$$\mathfrak{Find}\:\mathfrak{the}\:\mathfrak{surface}\:\mathfrak{area}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{solid}\:\mathfrak{generated} \\ $$$$\:\:\mathfrak{by}\:\mathfrak{the}\:\mathfrak{revolution}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{cardioids}\:\mathfrak{r}=\mathfrak{a}\left(\mathrm{1}+\mathfrak{cos}\:\theta\right)\:\mathfrak{about}\:\mathfrak{the}\:\mathfrak{initial}\:\mathfrak{line}. \\ $$

Question Number 83603 Answers: 0 Comments: 4

∫ (dx/(1−2cos x))

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

Question Number 83597 Answers: 0 Comments: 1

∫_0 ^2 (3x^2 −4x+2)dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{2}\right){dx} \\ $$

Question Number 83569 Answers: 0 Comments: 1

calculate ∫_1 ^(+∞) (dx/(x^4 (3x−1)^5 ))

$${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{4}} \left(\mathrm{3}{x}−\mathrm{1}\right)^{\mathrm{5}} } \\ $$

Question Number 83521 Answers: 0 Comments: 1

∫((√(sin(x)))/(sin^2 (x)+1)) dx

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

Question Number 83488 Answers: 1 Comments: 0

∫ ((x^3 −1)/(√(x^2 −1))) dx = ?

$$\int\:\frac{\mathrm{x}^{\mathrm{3}} −\mathrm{1}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 83441 Answers: 1 Comments: 0

calculate ∫_0 ^(π/4) (√(1+2tanx))dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \sqrt{\mathrm{1}+\mathrm{2}{tanx}}{dx} \\ $$

Question Number 83440 Answers: 0 Comments: 0

find ∫_0 ^(π/2) (dx/(sinx^(cosx) +cosx^(sinx) ))

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{{sinx}^{{cosx}} +{cosx}^{{sinx}} } \\ $$

Question Number 83405 Answers: 0 Comments: 2

lim_(b→1^− ) ∫_0 ^b ((sin (x))/(√(1−x^2 ))) dx ?

$$\underset{\mathrm{b}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{b}} \:\frac{\mathrm{sin}\:\left(\mathrm{x}\right)}{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:?\: \\ $$

Question Number 83385 Answers: 2 Comments: 1

∫((1+ae^(−(a+1)x) +(a+1)e^(−ax) )/x^2 ) dx, a∈z^+

$$\int\frac{\mathrm{1}+{ae}^{−\left({a}+\mathrm{1}\right){x}} +\left({a}+\mathrm{1}\right){e}^{−{ax}} }{{x}^{\mathrm{2}} }\:{dx},\:\:{a}\in{z}^{+} \\ $$

Question Number 83383 Answers: 1 Comments: 0

find ∫_0 ^2 ∫_0 ^(√(4−x^2 )) ∫_0 ^(2−z) zdxdydz pleas help me sir

$${find}\:\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} \int_{\mathrm{0}} ^{\mathrm{2}−{z}} {zdxdydz} \\ $$$${pleas}\:{help}\:{me}\:{sir} \\ $$

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