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IntegrationQuestion and Answers: Page 199

Question Number 74344    Answers: 1   Comments: 1

calculate ∫ ((x^2 −x+3)/(x^3 (x+2)^2 ))dx

$${calculate}\:\int\:\:\:\:\:\frac{{x}^{\mathrm{2}} −{x}+\mathrm{3}}{{x}^{\mathrm{3}} \left({x}+\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 74343    Answers: 0   Comments: 1

calculatef(α)= ∫_0 ^∞ ((arctan(αx^2 ))/(x^2 +9))dx with α real.

$${calculatef}\left(\alpha\right)=\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\alpha{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx}\:\:\:{with}\:\alpha\:{real}. \\ $$

Question Number 74334    Answers: 0   Comments: 1

∫te^t cos e^t .e^t dt

$$\int{te}^{{t}} \mathrm{cos}\:{e}^{{t}} .{e}^{{t}} {dt} \\ $$

Question Number 74320    Answers: 0   Comments: 0

∫_0 ^x x e^x (cos e^x )e^x dx

$$\int_{\mathrm{0}} ^{{x}} {x}\:{e}^{{x}} \left(\mathrm{cos}\:\:{e}^{{x}} \right){e}^{{x}} {dx} \\ $$

Question Number 74264    Answers: 0   Comments: 1

∫_0 ^x xe^x sin e^x e^x dx

$$\int_{\mathrm{0}} ^{{x}} {xe}^{{x}} \mathrm{sin}\:{e}^{{x}} {e}^{{x}} {dx} \\ $$

Question Number 74263    Answers: 0   Comments: 1

∫_0 ^x e^x cos e^x e^x dx

$$\int_{\mathrm{0}} ^{{x}} {e}^{{x}} \mathrm{cos}\:{e}^{{x}} {e}^{{x}} {dx} \\ $$

Question Number 74231    Answers: 1   Comments: 2

Question Number 74224    Answers: 1   Comments: 2

find ∫ (x^2 +1)^(1/4) cos((1/2)arctan((1/x)))dx and ∫ (x^2 +1)^(1/4) sin((1/2)arctan((1/x)))dx

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

Question Number 74223    Answers: 1   Comments: 0

calculate f(a)=∫_0 ^1 (√(x^2 +ax+1))dx and g(a)=∫_0 ^1 ((xdx)/(√(x^2 +ax+1))) with ∣a∣<2 2)find the value of ∫_0 ^1 (√(x^2 +(√2)x+1))dx and ∫_0 ^1 ((xdx)/(√(x^2 +(√2)x+1)))

$${calculate}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}{dx}\:\:\:{and}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}} \\ $$$${with}\:\:\mid{a}\mid<\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}{dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}} \\ $$

Question Number 74218    Answers: 1   Comments: 0

verify that y(x)=e^x (cos e^x −e^x sin e^x ) is the solution of integral equation y(x)=(1−xe^(2x) )cos 1−e^(2x) sin 1+∫_0 ^x {1−(x−t)e^(2x) }y(t)dt

$${verify}\:{that}\:{y}\left({x}\right)={e}^{{x}} \left(\mathrm{cos}\:{e}^{{x}} −{e}^{{x}} \mathrm{sin}\:{e}^{{x}} \right)\:{is}\:{the}\:{solution}\:{of}\:{integral}\:{equation}\:{y}\left({x}\right)=\left(\mathrm{1}−{xe}^{\mathrm{2}{x}} \right)\mathrm{cos}\:\mathrm{1}−{e}^{\mathrm{2}{x}} \mathrm{sin}\:\mathrm{1}+\underset{\mathrm{0}} {\overset{{x}} {\int}}\left\{\mathrm{1}−\left({x}−{t}\right){e}^{\mathrm{2}{x}} \right\}{y}\left({t}\right){dt} \\ $$

Question Number 74210    Answers: 1   Comments: 0

∫e^t cos e^t dt

$$\int{e}^{{t}} \mathrm{cos}\:{e}^{{t}} {dt} \\ $$

Question Number 74131    Answers: 0   Comments: 2

Can anyone share the solutions (pdf) of the book Advanced engineering Mathematics by Erwin kreyzig 8th edition ?

$${Can}\:{anyone}\:{share}\:{the}\:{solutions}\:\left({pdf}\right) \\ $$$${of}\:{the}\:{book}\:{Advanced}\:{engineering} \\ $$$${Mathematics}\:{by}\:{Erwin}\:{kreyzig}\:\mathrm{8}{th} \\ $$$${edition}\:? \\ $$$$ \\ $$

Question Number 74117    Answers: 0   Comments: 1

Find the volume of the solid that lies within the sphere x^2 +y^2 +z^2 =16, above the x-y plane and below the cone z=(√(x^2 +y^2 ))

$${Find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\:{that}\:{lies} \\ $$$${within}\:{the}\:{sphere}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{16},\:{above} \\ $$$${the}\:{x}-{y}\:{plane}\:{and}\:{below}\:{the}\:{cone} \\ $$$${z}=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$

Question Number 74068    Answers: 1   Comments: 4

Question Number 74040    Answers: 1   Comments: 1

Find orthogonal trajectories of the curves: (x−c)^2 +y^2 =c^2 .

$${Find}\:{orthogonal}\:{trajectories}\:{of}\:{the} \\ $$$${curves}:\:\left({x}−{c}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} ={c}^{\mathrm{2}} . \\ $$

Question Number 74037    Answers: 1   Comments: 0

∫_0^ ^(Π/2) xcos^n xdx by reduction formula

$$\int_{\mathrm{0}^{} } ^{\Pi/\mathrm{2}} {x}\mathrm{cos}^{{n}} {xdx}\:\:\:{by}\:{reduction}\:{formula} \\ $$

Question Number 73832    Answers: 2   Comments: 7

Question Number 74338    Answers: 0   Comments: 0

∫e^(2t) sin e^t dt

$$\int{e}^{\mathrm{2}{t}} \mathrm{sin}\:{e}^{{t}} {dt} \\ $$

Question Number 73804    Answers: 0   Comments: 0

Question Number 73751    Answers: 1   Comments: 1

Find out the value of J=∫_0 ^∞ ∫_0 ^1 (2e^(−2xy) −e^(−xy) )dxdy

$${Find}\:\:{out}\:{the}\:{value}\:{of}\:\:\: \\ $$$$\:\:{J}=\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{2}{e}^{−\mathrm{2}{xy}} −{e}^{−{xy}} \right){dxdy}\: \\ $$

Question Number 73715    Answers: 1   Comments: 2

Evaluate the integral : ∫_( R) ∫(3x^2 +14xy+8y^2 )dxdy for the region R in the 1st quadrant bounded by the lines y=((−3)/2)x+1,y=((−3)/2)x+3,y=−(1/4)x and y=−(1/4)x+1 .

$${Evaluate}\:{the}\:{integral}\:: \\ $$$$\underset{\:\mathbb{R}} {\int}\int\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{14}{xy}+\mathrm{8}{y}^{\mathrm{2}} \right){dxdy}\:{for}\:{the}\:{region} \\ $$$$\mathbb{R}\:\mathrm{in}\:{the}\:\mathrm{1}{st}\:{quadrant}\:{bounded}\:{by}\:{the} \\ $$$${lines}\:{y}=\frac{−\mathrm{3}}{\mathrm{2}}{x}+\mathrm{1},{y}=\frac{−\mathrm{3}}{\mathrm{2}}{x}+\mathrm{3},{y}=−\frac{\mathrm{1}}{\mathrm{4}}{x} \\ $$$${and}\:{y}=−\frac{\mathrm{1}}{\mathrm{4}}{x}+\mathrm{1}\:. \\ $$

Question Number 73689    Answers: 2   Comments: 0

∫_(−1) ^( 1) (2+x)sin^(−1) (((√(3−3x^2 ))/(2+x)))dx = ?

$$\int_{−\mathrm{1}} ^{\:\:\mathrm{1}} \left(\mathrm{2}+{x}\right)\mathrm{sin}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{3}−\mathrm{3}{x}^{\mathrm{2}} }}{\mathrm{2}+{x}}\right){dx}\:=\:? \\ $$

Question Number 73545    Answers: 1   Comments: 2

evaluate ∫lnx dx

$${evaluate}\:\:\int{lnx}\:{dx} \\ $$

Question Number 73489    Answers: 0   Comments: 0

calculate ∫_0 ^∞ ((arctan(3+x^2 ))/((2 x^2 +9)^2 ))dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left(\mathrm{3}+{x}^{\mathrm{2}} \right)}{\left(\mathrm{2}\:{x}^{\mathrm{2}} +\mathrm{9}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 73484    Answers: 1   Comments: 0

decompose inside C(x) the fraction F(x)=(1/((x^2 +1)^n )) calculate ∫_0 ^∞ F(x)dx

$${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{{n}} } \\ $$$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{F}\left({x}\right){dx} \\ $$

Question Number 73483    Answers: 1   Comments: 0

find ∫ (dx/(x+2−(√(x^2 −x +7))))

$${find}\:\int\:\:\:\:\frac{{dx}}{{x}+\mathrm{2}−\sqrt{{x}^{\mathrm{2}} −{x}\:+\mathrm{7}}} \\ $$

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