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IntegrationQuestion and Answers: Page 22

Question Number 191811 Answers: 2 Comments: 0

∫x^2 e^(−x) dx=?

$$\int{x}^{\mathrm{2}} {e}^{−{x}} {dx}=? \\ $$

Question Number 191567 Answers: 1 Comments: 0

Question Number 191519 Answers: 1 Comments: 0

∫_0 ^( (π/2)) (dx/(1+ sin x))

$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{\mathrm{1}+\:\mathrm{sin}\:{x}} \\ $$

Question Number 191369 Answers: 1 Comments: 0

calculate 𝛗= Σ_(n=1) ^∞ (( sin(((nπ)/3) ))/((2n + 1 )^( 2) ))= ?

$$ \\ $$$$\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\:{sin}\left(\frac{{n}\pi}{\mathrm{3}}\:\right)}{\left(\mathrm{2}{n}\:+\:\mathrm{1}\:\right)^{\:\mathrm{2}} }=\:? \\ $$$$ \\ $$

Question Number 191342 Answers: 1 Comments: 0

calculate... Ω ={ ∫_0 ^( (π/4)) ( 1 + (√3) sin(x) + cos(x) )^( n) dx}^(1/n) = ?

$$ \\ $$$$\:\:\:\:{calculate}... \\ $$$$\:\Omega\:=\left\{\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \left(\:\:\mathrm{1}\:+\:\sqrt{\mathrm{3}}\:{sin}\left({x}\right)\:+\:{cos}\left({x}\right)\:\right)^{\:{n}} {dx}\right\}^{\frac{\mathrm{1}}{{n}}} =\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 191303 Answers: 2 Comments: 0

Question Number 191188 Answers: 1 Comments: 0

∫ (((2−x)/(1−x)))^(1/4) dx =?

$$\:\:\:\:\:\:\:\:\:\:\:\int\:\sqrt[{\mathrm{4}}]{\frac{\mathrm{2}−\mathrm{x}}{\mathrm{1}−\mathrm{x}}}\:\mathrm{dx}\:=?\: \\ $$

Question Number 191142 Answers: 0 Comments: 0

Question Number 191049 Answers: 1 Comments: 1

Question Number 191041 Answers: 1 Comments: 2

Question Number 190987 Answers: 1 Comments: 0

Question Number 190984 Answers: 2 Comments: 0

∫_0 ^3 ∫_0 ^2 x^2 ydydx

$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{3}} \int_{\mathrm{0}} ^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} \mathrm{ydydx}\: \\ $$$$ \\ $$

Question Number 190983 Answers: 0 Comments: 0

∫_(x= ) ^ ∫_(y= ) ^( −x) ∫_(z= ) ^( −x−y) xdzdydx

$$ \\ $$$$\:\:\:\:\int_{\boldsymbol{{x}}= } ^{ } \int_{\boldsymbol{{y}}= } ^{ −\boldsymbol{{x}}} \int_{\boldsymbol{{z}}= } ^{ −\boldsymbol{{x}}−\boldsymbol{{y}}} \boldsymbol{{xdzdydx}} \\ $$$$ \\ $$

Question Number 190940 Answers: 1 Comments: 0

The parametric equation of a curve are x=3t^2 and y=3t−t^2 . Find the volume generated when the plane bounded by the curve ,the x−axis and the ordinates corresponding to t=0 and t=2 rotates about the y−axis

$$\mathrm{The}\:\mathrm{parametric}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{curve}\:\:\mathrm{are} \\ $$$$\mathrm{x}=\mathrm{3t}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{y}=\mathrm{3t}−\mathrm{t}^{\mathrm{2}} . \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{generated} \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curve} \\ $$$$,\mathrm{the}\:\mathrm{x}−\mathrm{axis}\:\mathrm{and}\:\mathrm{the}\:\mathrm{ordinates}\: \\ $$$$\mathrm{corresponding}\:\mathrm{to}\: \\ $$$$\mathrm{t}=\mathrm{0}\:\:\:\mathrm{and}\:\mathrm{t}=\mathrm{2}\:\:\mathrm{rotates}\:\mathrm{about}\:\mathrm{the}\:\mathrm{y}−\mathrm{axis} \\ $$

Question Number 190937 Answers: 1 Comments: 0

Show that ∫ ((sech (√x) tanh (√x))/( (√x)))=−(2/(cosh (√x)))

$$\mathrm{Show}\:\:\mathrm{that}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\mathrm{sech}\:\sqrt{\mathrm{x}}\:\mathrm{tanh}\:\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{x}}}=−\frac{\mathrm{2}}{\mathrm{cosh}\:\sqrt{\mathrm{x}}} \\ $$

Question Number 190841 Answers: 1 Comments: 0

Question Number 190812 Answers: 1 Comments: 1

Question Number 190809 Answers: 0 Comments: 2

Question Number 190754 Answers: 1 Comments: 0

I = ∫_0 ^( π) e^(acos t) cos (asin t)dt

$$\:\:\:\:\:\:{I}\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\:\pi} {e}^{{a}\mathrm{cos}\:{t}} \:\mathrm{cos}\:\left({a}\mathrm{sin}\:\:{t}\right){dt} \\ $$

Question Number 190740 Answers: 1 Comments: 0

∫(dx/((x^2 +5)^2 ))=?

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

Question Number 190708 Answers: 1 Comments: 0

Question Number 190700 Answers: 1 Comments: 0

Question Number 190692 Answers: 1 Comments: 0

calculate 𝛗 = ∫_0 ^( ∞) (( sin^( 3) (x ) ln( x ))/x) dx = ? @ nice − mathematics

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{calculate}\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\mathrm{sin}^{\:\mathrm{3}} \left({x}\:\right)\:\mathrm{ln}\left(\:{x}\:\right)}{{x}}\:\mathrm{d}{x}\:=\:?\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:@\:\mathrm{nice}\:−\:\mathrm{mathematics}\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 190624 Answers: 2 Comments: 0

Question Number 190623 Answers: 2 Comments: 0

calculate : Σ_(n=1) ^∞ (( (−1)^( n−1) )/n) cos ((( nπ)/3) ) =?

$$ \\ $$$$\:\:\:\:\:\:\mathrm{calculate}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} }{{n}}\:\mathrm{cos}\:\left(\frac{\:{n}\pi}{\mathrm{3}}\:\right)\:=? \\ $$$$ \\ $$

Question Number 190622 Answers: 1 Comments: 0

prove : ∫_(−∞) ^( ∞) ((( x)/( ⋮ )^2 dx= Σ_(k=1) ^∞ (1/( k^2 )) ⋖))

$$ \\ $$$$\:\:\:{prove}\:: \\ $$$$\:\:\int_{−\infty} ^{\:\infty} \:\:\:\left(\frac{\:{x}}{\left.\:\underline{\vdots} \right)^{\mathrm{2}} \mathrm{d}{x}=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\:{k}\:^{\mathrm{2}} }\:\:\:\lessdot}\right. \\ $$

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