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IntegrationQuestion and Answers: Page 30

Question Number 194850    Answers: 0   Comments: 0

Question Number 194785    Answers: 0   Comments: 0

∫∫ x^2 +y^2 dxdy (D=x^4 +y^4 ≤1)

$$\int\int\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:{dxdy}\:\left({D}={x}^{\mathrm{4}} +{y}^{\mathrm{4}} \leqslant\mathrm{1}\right) \\ $$

Question Number 194759    Answers: 1   Comments: 1

∫_0 ^( 1) ∫_0 ^( 1) (((1+x^2 )/(1+x^2 +y^2 ))) dxdy

$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\frac{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\right)\:\mathrm{dxdy}\: \\ $$

Question Number 194591    Answers: 0   Comments: 0

∫_(−2) ^2 ∫_(2x^2 ) ^8 ∫_(−(√((1/2)y−x^2 ))) ^(√((1/2)y−x^2 )) ((√(3x^2 +3z^2 )) )dzdydx

$$\:\:\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\:\underset{\mathrm{2x}^{\mathrm{2}} } {\overset{\mathrm{8}} {\int}}\:\:\underset{−\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}−\mathrm{x}^{\mathrm{2}} }} {\overset{\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}−\mathrm{x}^{\mathrm{2}} }} {\int}}\:\left(\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{3z}^{\mathrm{2}} }\:\right)\mathrm{dzdydx} \\ $$

Question Number 194548    Answers: 2   Comments: 1

Question Number 194515    Answers: 1   Comments: 0

∣∫f(x)dx∣=∫∣f(x)∣dx

$$\mid\int{f}\left({x}\right){dx}\mid=\int\mid{f}\left({x}\right)\mid{dx} \\ $$

Question Number 194456    Answers: 2   Comments: 0

$$\:\:\:\:\:\:\cancel{ } \\ $$

Question Number 194412    Answers: 1   Comments: 0

Question Number 194388    Answers: 0   Comments: 0

∫(((1+x^2 )sin x+4cos x)/(2(1+x^2 )^3 )) dx

$$\int\frac{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\mathrm{sin}\:{x}+\mathrm{4cos}\:{x}}{\mathrm{2}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:{dx} \\ $$

Question Number 193982    Answers: 3   Comments: 0

∫ ((6x^3 +9x^2 +15x+6)/( (√(x^2 +x+1)))) dx =?

$$\:\:\:\:\:\int\:\frac{\mathrm{6x}^{\mathrm{3}} +\mathrm{9x}^{\mathrm{2}} +\mathrm{15x}+\mathrm{6}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}}\:\mathrm{dx}\:=? \\ $$

Question Number 193852    Answers: 3   Comments: 0

Question Number 193538    Answers: 2   Comments: 0

∫ (dx/(x^6 +1)) =?

$$\:\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{6}} +\mathrm{1}}\:=? \\ $$

Question Number 193526    Answers: 2   Comments: 0

Question Number 193512    Answers: 1   Comments: 0

Question Number 193439    Answers: 1   Comments: 2

∫^(π/2) _( 0) (((tanx))^(1/3) /((sinx+cosx)^2 ))dx

$$\underset{\:\:\mathrm{0}} {\int}^{\pi/\mathrm{2}} \frac{\sqrt[{\mathrm{3}}]{{tanx}}}{\left({sinx}+{cosx}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 193409    Answers: 0   Comments: 0

⋐

$$\:\:\:\Subset \\ $$

Question Number 193377    Answers: 1   Comments: 1

Evaluate I=∫_0 ^( ∞) (1/(x^5 +x^4 +x^3 +x^2 +x+1))dx

$${Evaluate} \\ $$$${I}=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}}{{x}^{\mathrm{5}} +{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\ $$

Question Number 193307    Answers: 0   Comments: 0

Question Number 193278    Answers: 1   Comments: 0

Please Help...!! ∫^( ∞) _( 0) x.e^(−x) .sinx.dx

$${Please}\:{Help}...!! \\ $$$$\:\:\:\:\underset{\:\:\:\:\mathrm{0}} {\int}^{\:\:\infty} {x}.{e}^{−{x}} .{sinx}.{dx}\: \\ $$$$ \\ $$

Question Number 193231    Answers: 1   Comments: 0

Question Number 193214    Answers: 0   Comments: 0

Evaluate Ω=∫_(−∞) ^( ∞) ((e^(x/2) ln((√((3−x)/(3+x)))))/(tanh^(−1) ((x/3))(1+e^x )))dx

$${Evaluate} \\ $$$$\Omega=\int_{−\infty} ^{\:\infty} \frac{{e}^{\frac{{x}}{\mathrm{2}}} {ln}\left(\sqrt{\frac{\mathrm{3}−{x}}{\mathrm{3}+{x}}}\right)}{{tanh}^{−\mathrm{1}} \left(\frac{{x}}{\mathrm{3}}\right)\left(\mathrm{1}+{e}^{{x}} \right)}{dx} \\ $$

Question Number 193036    Answers: 1   Comments: 0

if f(x)=x(√((16−x^2 )^3 )) find ∫_(0.5) ^(3.5) f(x) dx using trapezoidal method then find the max and min value of the error with the given n steps x_n f(x_n ) −− −−− 0.5 31.24 0.93 54.69 1.36 72.3 1.79 81.98 2.21 81.25 2.64 71.54 3.07 51.68 3.5 25.41

$${if}\:{f}\left({x}\right)={x}\sqrt{\left(\mathrm{16}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$$${find}\:\int_{\mathrm{0}.\mathrm{5}} ^{\mathrm{3}.\mathrm{5}} {f}\left({x}\right)\:{dx}\:{using}\:{trapezoidal}\:{method} \\ $$$${then}\:{find}\:{the}\:{max}\:{and}\:{min}\:{value}\:{of}\:{the}\:{error} \\ $$$$\:{with}\:{the}\:{given}\:{n}\:{steps} \\ $$$${x}_{{n}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}_{{n}} \right) \\ $$$$−−\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−− \\ $$$$\mathrm{0}.\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{31}.\mathrm{24} \\ $$$$\mathrm{0}.\mathrm{93}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{54}.\mathrm{69} \\ $$$$\mathrm{1}.\mathrm{36}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{72}.\mathrm{3} \\ $$$$\mathrm{1}.\mathrm{79}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{81}.\mathrm{98} \\ $$$$\mathrm{2}.\mathrm{21}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{81}.\mathrm{25} \\ $$$$\mathrm{2}.\mathrm{64}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{71}.\mathrm{54} \\ $$$$\mathrm{3}.\mathrm{07}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{51}.\mathrm{68} \\ $$$$\mathrm{3}.\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{25}.\mathrm{41} \\ $$$$ \\ $$

Question Number 192933    Answers: 2   Comments: 0

Question Number 192916    Answers: 2   Comments: 0

Question Number 192849    Answers: 0   Comments: 0

Question Number 192770    Answers: 1   Comments: 4

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