Question and Answers Forum

IntegrationQuestion and Answers: Page 163

Question Number 101057 Answers: 1 Comments: 0

Find the area bounded the curves f(x)= ∣x^3 −4x^2 +3x∣ and x−axis

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded}\:\mathrm{the}\: \\ $$$$\mathrm{curves}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mid{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} +\mathrm{3}{x}\mid\:\mathrm{and}\: \\ $$$$\mathrm{x}−\mathrm{axis}\: \\ $$

Question Number 101079 Answers: 2 Comments: 2

Question Number 101023 Answers: 0 Comments: 0

∫tan^(1/5) x cotx secxdx

$$\int{tan}^{\frac{\mathrm{1}}{\mathrm{5}}} {x}\:{cotx}\:{secxdx} \\ $$

Question Number 101014 Answers: 0 Comments: 0

Show that ∫_(−∞) ^(+∞) (dx/(1+(x+tanx)^2 )) = π

$${Show}\:{that} \\ $$$$\int_{−\infty} ^{+\infty} \frac{{dx}}{\mathrm{1}+\left({x}+{tanx}\right)^{\mathrm{2}} }\:\:\:=\:\:\:\pi \\ $$

Question Number 101011 Answers: 0 Comments: 5

∫_0 ^∞ ((sinx)/x)dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}}{{x}}{dx} \\ $$

Question Number 101018 Answers: 0 Comments: 0

∫_(−∞) ^∞ ((log(sin^2 x))/(1+x+e^x ))dx

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

Question Number 100969 Answers: 1 Comments: 0

find ∫_(−∞) ^∞ ((sin(cosx))/((x^2 −x+1)^2 ))dx

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

Question Number 100967 Answers: 1 Comments: 0

calculate ∫_0 ^(π/2) ln(2+ sinθ)dθ

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{2}+\:\mathrm{sin}\theta\right)\mathrm{d}\theta \\ $$

Question Number 100965 Answers: 0 Comments: 0

calculate ∫_0 ^π ln(x^2 −2xcosθ +1)dθ (x real)

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)\mathrm{d}\theta\:\:\:\:\left(\mathrm{x}\:\mathrm{real}\right) \\ $$

Question Number 100956 Answers: 2 Comments: 0

Question Number 100948 Answers: 0 Comments: 1

Question Number 100829 Answers: 0 Comments: 0

hello every one prove that ∫_0 ^(π/2) cos^u (x) cos(ax) arctan(b cos(x)) dx =((2^(−u−2) .π.b.Γ(u+2))/(Γ(((u−a+3)/2))Γ(((u+a+3)/2)))).x_4 F_3 ((((1/2),1+(u/2),((u+3)/2),−b^2 )),(((3/2),((u−a+3)/2),((u+a+3)/2))) ) Re u>−1 ,∣arg(1+b^2 ) ∣<π

$${hello}\:{every}\:{one}\: \\ $$$$ \\ $$$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {cos}^{{u}} \left({x}\right)\:{cos}\left({ax}\right)\:{arctan}\left({b}\:{cos}\left({x}\right)\right)\:{dx} \\ $$$$=\frac{\mathrm{2}^{−{u}−\mathrm{2}} .\pi.{b}.\Gamma\left({u}+\mathrm{2}\right)}{\Gamma\left(\frac{{u}−{a}+\mathrm{3}}{\mathrm{2}}\right)\Gamma\left(\frac{{u}+{a}+\mathrm{3}}{\mathrm{2}}\right)}.{x}_{\mathrm{4}} {F}_{\mathrm{3}} \begin{pmatrix}{\frac{\mathrm{1}}{\mathrm{2}},\mathrm{1}+\frac{{u}}{\mathrm{2}},\frac{{u}+\mathrm{3}}{\mathrm{2}},−{b}^{\mathrm{2}} }\\{\frac{\mathrm{3}}{\mathrm{2}},\frac{{u}−{a}+\mathrm{3}}{\mathrm{2}},\frac{{u}+{a}+\mathrm{3}}{\mathrm{2}}}\end{pmatrix} \\ $$$$ \\ $$$$ \\ $$$${Re}\:{u}>−\mathrm{1}\:,\mid{arg}\left(\mathrm{1}+{b}^{\mathrm{2}} \right)\:\mid<\pi \\ $$$$ \\ $$

Question Number 100789 Answers: 2 Comments: 0