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IntegrationQuestion and Answers: Page 199

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

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

Question Number 83367 Answers: 0 Comments: 1

∫_(−∞) ^∞ ((sin^7 (x))/x^7 )dx

$$\int_{−\infty} ^{\infty} \frac{{sin}^{\mathrm{7}} \left({x}\right)}{{x}^{\mathrm{7}} }{dx} \\ $$

Question Number 83342 Answers: 1 Comments: 0

∫_0 ^1 ∫_0 ^( z) ∫_y ^1 ((z^(n+1) Li_1 (y))/((zx)^2 ))dx dy dz , ∀ n∈z

$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\:{z}} \int_{{y}} ^{\mathrm{1}} \frac{{z}^{{n}+\mathrm{1}} {Li}_{\mathrm{1}} \left({y}\right)}{\left({zx}\right)^{\mathrm{2}} }{dx}\:{dy}\:{dz}\:,\:\forall\:{n}\in{z} \\ $$

Question Number 83338 Answers: 1 Comments: 0

∫ sin (3x) tan (2x) dx ?

$$\int\:\mathrm{sin}\:\left(\mathrm{3x}\right)\:\mathrm{tan}\:\left(\mathrm{2x}\right)\:\mathrm{dx}\:? \\ $$

Question Number 83331 Answers: 1 Comments: 7

Question Number 83318 Answers: 0 Comments: 0

Evaluate ∫x^(1/x^n ) dx ,n>0

$${Evaluate} \\ $$$$\int{x}^{\frac{\mathrm{1}}{{x}^{{n}} }} \:{dx}\:,{n}>\mathrm{0} \\ $$

Question Number 83276 Answers: 1 Comments: 0

∫sec^5 3x•sec3xtan 3xdx

$$\int\mathrm{s}{ec}^{\mathrm{5}} \mathrm{3}{x}\bullet\mathrm{s}{ec}\mathrm{3}{x}\mathrm{tan}\:\mathrm{3}{xdx} \\ $$

Question Number 83259 Answers: 1 Comments: 0

∫x^9 sin x^(10) dx

$$\int{x}^{\mathrm{9}} \mathrm{sin}\:{x}^{\mathrm{10}} {dx} \\ $$

Question Number 83253 Answers: 0 Comments: 3

calculate ∫_0 ^∞ (dx/((x^4 −x^2 +1)^2 ))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 83252 Answers: 1 Comments: 1

calculate ∫_0 ^(π/2) (dx/(cos^2 x +(√3)sin^2 x))

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{{cos}^{\mathrm{2}} {x}\:+\sqrt{\mathrm{3}}{sin}^{\mathrm{2}} {x}} \\ $$

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