Question and Answers Forum

All Questions   Topic List

IntegrationQuestion and Answers: Page 166

Question Number 91771    Answers: 0   Comments: 1

∫_0 ^∞ ((sin^3 (x))/x^2 )dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 91753    Answers: 1   Comments: 3

∫3 (ln x)^2 dx = ??

$$\int\mathrm{3}\:\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} \:{dx}\:=\:?? \\ $$

Question Number 91735    Answers: 0   Comments: 1

∫_0 ^(π/2) ((tan^m α))^(1/k) dα for m>1

$$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \sqrt[{{k}}]{\mathrm{tan}^{{m}} \:\alpha}\:{d}\alpha\:{for}\:{m}>\mathrm{1} \\ $$

Question Number 91714    Answers: 0   Comments: 1

Question Number 91703    Answers: 0   Comments: 0

∫_(−∞) ^(+∞) f^2 (x)dx ∀f

$$\int_{−\infty} ^{+\infty} {f}^{\mathrm{2}} \left({x}\right){dx}\:\forall{f} \\ $$

Question Number 91668    Answers: 0   Comments: 0

∫e^x^2 erf(x) dx

$$\int{e}^{{x}^{\mathrm{2}} } \:{erf}\left({x}\right)\:{dx} \\ $$

Question Number 91641    Answers: 0   Comments: 0

find ∫ ((cos^4 x+sin^4 x)/(cos^3 x+sin^3 x))dx

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

Question Number 91636    Answers: 0   Comments: 0

∫(dx/(x((√x)+^5 (√x^2 ))))

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

Question Number 91630    Answers: 0   Comments: 1

show that ∫_(−(π/4)) ^(π/4) ((sin2x)/((2+cos2x)^2 ))ln(1+e^x )dx =(π/(16))−((π(√3))/(36))

$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin2x}}{\left(\mathrm{2}+\mathrm{cos2x}\right)^{\mathrm{2}} }\mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$$$=\frac{\pi}{\mathrm{16}}−\frac{\pi\sqrt{\mathrm{3}}}{\mathrm{36}} \\ $$

Question Number 91621    Answers: 0   Comments: 1

calculate ∫_0 ^∞ sin(x^6 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{\mathrm{6}} \right){dx} \\ $$

Question Number 91620    Answers: 0   Comments: 1

let f(x) =2 x−(√(x−1)) find ∫ ((f(x))/(f^(−1) (x)))dx and ∫ ln(((f(x))/(f^(−1) (x))))dx

$${let}\:{f}\left({x}\right)\:=\mathrm{2}\:{x}−\sqrt{{x}−\mathrm{1}} \\ $$$${find}\:\int\:\:\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}{dx}\:\:{and}\:\:\int\:{ln}\left(\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}\right){dx} \\ $$

Question Number 91619    Answers: 0   Comments: 1

calculate ∫_2 ^(+∞) (((−1)^([2x]) )/(x[x]−1))dx

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

Question Number 91615    Answers: 0   Comments: 2

hi every one is it right if we use tylor in this integration and if there were another way that will be very cool ∫sin(x^4 )dx

$${hi}\:{every}\:{one}\:{is}\:{it}\:{right}\:{if}\:{we}\:{use}\:{tylor} \\ $$$${in}\:{this}\:{integration}\:{and}\:{if}\:{there}\:{were} \\ $$$${another}\:{way}\:{that}\:{will}\:{be}\:{very}\:{cool} \\ $$$$\int{sin}\left({x}^{\mathrm{4}} \right){dx}\: \\ $$$$ \\ $$$$ \\ $$

Question Number 91611    Answers: 0   Comments: 1

find the volume of the region between curves (xy=4 and x+y=5) revolvex around the X axis

$$\:{find}\:{the}\:{volume}\:{of}\:{the}\:{region}\: \\ $$$${between}\:{curves}\:\left({xy}=\mathrm{4}\:{and}\:{x}+{y}=\mathrm{5}\right) \\ $$$${revolvex}\:{around}\:{the}\:{X}\:{axis} \\ $$

Question Number 91603    Answers: 0   Comments: 1

calculate ∫_0 ^∞ xe^(−x^2 −[x]) dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} {xe}^{−{x}^{\mathrm{2}} −\left[{x}\right]} \:{dx} \\ $$

Question Number 91593    Answers: 1   Comments: 0

∫ ((sec x csc x dx)/(ln(tan^2 x))) ?

$$\int\:\frac{\mathrm{sec}\:{x}\:{csc}\:{x}\:{dx}}{\mathrm{ln}\left(\mathrm{tan}\:^{\mathrm{2}} {x}\right)}\:? \\ $$

Question Number 91555    Answers: 1   Comments: 4

Question Number 91542    Answers: 2   Comments: 3

∫ (x^3 /(2x+1)) dx = ?

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

Question Number 91534    Answers: 0   Comments: 3

∫_1 ^∞ ((sin^2 (x))/x^2 )dx

$$\int_{\mathrm{1}} ^{\infty} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 91479    Answers: 1   Comments: 4

∫_(−π/2 ) ^(π/2) (√(cos x−cos^3 x)) dx=...

$$\:\underset{−\pi/\mathrm{2}\:} {\overset{\pi/\mathrm{2}} {\int}}\:\sqrt{\mathrm{cos}\:{x}−\mathrm{cos}^{\mathrm{3}} {x}}\:\mathrm{dx}=... \\ $$

Question Number 91326    Answers: 2   Comments: 1

Question Number 91310    Answers: 0   Comments: 0

show that ∫_0 ^(π/2) cot (x) ln(sec(x)) dx=(π^2 /(24))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {cot}\:\left({x}\right)\:{ln}\left({sec}\left({x}\right)\right)\:{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{24}} \\ $$

Question Number 91308    Answers: 0   Comments: 2

∫ (x^2 /(x^4 −x^2 −2)) dx ?

$$\int\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} −\mathrm{2}}\:{dx}\:? \\ $$

Question Number 91290    Answers: 0   Comments: 1

Question Number 91271    Answers: 1   Comments: 1

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

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

Question Number 91270    Answers: 0   Comments: 0

find ∫_0 ^∞ ((arctan(x+(1/x)))/(x^2 +1))dx

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

  Pg 161      Pg 162      Pg 163      Pg 164      Pg 165      Pg 166      Pg 167      Pg 168      Pg 169      Pg 170   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com