Question and Answers Forum

All Questions Topic List

IntegrationQuestion and Answers: Page 300

Question Number 31073 Answers: 1 Comments: 1

find I= ∫_0 ^(π/2) ((1−sinθ)/(cosθ))dθ .

$${find}\:{I}=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{\mathrm{1}−{sin}\theta}{{cos}\theta}{d}\theta\:. \\ $$

Question Number 31072 Answers: 0 Comments: 0

find ∫_0 ^∞ (dx/(e^x (√(sh(2x))))) dx.

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{e}^{{x}} \sqrt{{sh}\left(\mathrm{2}{x}\right)}}\:{dx}. \\ $$

Question Number 31071 Answers: 1 Comments: 3

find ∫_0 ^π (dx/(1+sin^2 x)) .

$${find}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{dx}}{\mathrm{1}+{sin}^{\mathrm{2}} {x}}\:. \\ $$

Question Number 31070 Answers: 0 Comments: 1

calculate ∫_0 ^π (dx/(1+2cosx)) .

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+\mathrm{2}{cosx}}\:. \\ $$

Question Number 31069 Answers: 1 Comments: 1

clculate ∫_0 ^1 x(√(x^2 −2x+2)) dx

$${clculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}\sqrt{{x}^{\mathrm{2}} \:−\mathrm{2}{x}+\mathrm{2}}\:{dx} \\ $$

Question Number 31068 Answers: 0 Comments: 0

find I_n =∫_(−(π/2)) ^(π/2) e^(−ax) cos^(2n) xdx .

$${find}\:\:{I}_{{n}} =\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \:{e}^{−{ax}} \:{cos}^{\mathrm{2}{n}} {xdx}\:\:. \\ $$

Question Number 31067 Answers: 0 Comments: 0

find A_n =∫_0 ^∞ x^(2n) e^(−ax^2 ) dx.

$${find}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{x}^{\mathrm{2}{n}} \:{e}^{−{ax}^{\mathrm{2}} } {dx}. \\ $$

Question Number 31066 Answers: 0 Comments: 0

find I_n =∫_0 ^(π/2) cos^(2n+1) xdx.

$${find}\:\:{I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{\mathrm{2}{n}+\mathrm{1}} {xdx}. \\ $$

Question Number 31065 Answers: 0 Comments: 0

find ∫_0 ^π ((xsinx)/((1−acosx)^2 )) dx with ∣a∣<1.

$${find}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{xsinx}}{\left(\mathrm{1}−{acosx}\right)^{\mathrm{2}} }\:{dx}\:{with}\:\:\mid{a}\mid<\mathrm{1}. \\ $$

Question Number 31063 Answers: 0 Comments: 0

find f(t)= ∫_0 ^1 ln(1+tx^2 )dxfor t>−1

$${find}\:{f}\left({t}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}+{tx}^{\mathrm{2}} \right){dxfor}\:\:{t}>−\mathrm{1} \\ $$

Question Number 31062 Answers: 0 Comments: 0

find ∫_0 ^(π/2) e^x sinx cos^2 xdx.

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{e}^{{x}} \:{sinx}\:{cos}^{\mathrm{2}} {xdx}. \\ $$

Question Number 31061 Answers: 0 Comments: 0

find ∫_0 ^(π/2) (sinθ −cosθ)ln(sinθ+cosθ)dθ.

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

Question Number 31060 Answers: 0 Comments: 0

calculate by recurrence ∫_0 ^∞ ((lnx)/((1+x)^n ))dx with n≥2 .

$${calculate}\:{by}\:{recurrence}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{lnx}}{\left(\mathrm{1}+{x}\right)^{{n}} }{dx}\:{with}\:{n}\geqslant\mathrm{2}\:. \\ $$

Question Number 31059 Answers: 0 Comments: 0

find ∫_0 ^(π/2) cos(2θ)ln(tanθ)dθ.

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}\left(\mathrm{2}\theta\right){ln}\left({tan}\theta\right){d}\theta. \\ $$

Question Number 31058 Answers: 0 Comments: 0

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

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

Question Number 31057 Answers: 0 Comments: 0

find ∫_0 ^1 (((√(1+x^2 )) −(√(1−x^2 )))/x^2 ) dx.

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{{x}^{\mathrm{2}} }\:{dx}.\: \\ $$

Question Number 31056 Answers: 0 Comments: 1

find ∫_1 ^(+∞) (dx/(x^2 −2xcosα +1)) with 0<α<π .

$${find}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:−\mathrm{2}{xcos}\alpha\:+\mathrm{1}}\:\:{with}\:\mathrm{0}<\alpha<\pi\:. \\ $$

Question Number 31055 Answers: 0 Comments: 1

find ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)(x^2 −2x+4))) .

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

Question Number 31054 Answers: 0 Comments: 0

find ∫_0 ^1 (dx/(x^4 +1)) .

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}}\:. \\ $$

Question Number 31053 Answers: 0 Comments: 1

let λ ∈R and a>0 find ∫_0 ^∞ e^(−ax) cos(λx)dx .

$${let}\:\lambda\:\in{R}\:{and}\:{a}>\mathrm{0}\:\:{find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{ax}} {cos}\left(\lambda{x}\right){dx}\:. \\ $$

Question Number 31052 Answers: 0 Comments: 0

let give 0<a<b find ∫_a ^b ((lnx)/x)dx .

$${let}\:{give}\:\mathrm{0}<{a}<{b}\:\:{find}\:\int_{{a}} ^{{b}} \:\:\frac{{lnx}}{{x}}{dx}\:. \\ $$

Question Number 31051 Answers: 0 Comments: 0

study the convergence of ∫_0 ^∞ ((e^(−ax) −e^(−bx) )/(1− e^(−x) )) dx.

$${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{ax}} \:−{e}^{−{bx}} }{\mathrm{1}−\:{e}^{−{x}} }\:{dx}. \\ $$

Question Number 31049 Answers: 0 Comments: 0

study the convergence of ∫_0 ^∞ x^(−x) dx .

$${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{x}^{−{x}} {dx}\:. \\ $$

Question Number 31048 Answers: 0 Comments: 0

study the convergence of ∫_1 ^(+∞) (((π/2) −arctanx)/x)dx

$${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{\frac{\pi}{\mathrm{2}}\:−{arctanx}}{{x}}{dx} \\ $$

Question Number 31145 Answers: 1 Comments: 0

Given ∫_0 ^1 f(x) dx = (((2018)),(( 0)) ) + (1/2) (((2018)),(( 1)) ) + (1/3) (((2018)),(( 2)) ) + ... + (1/(2019)) (((2018)),((2018)) ) ∫_0 ^1 g(x) dx = (((2018)),(( 0)) ) − (1/2) (((2018)),(( 1)) ) + (1/3) (((2018)),(( 2)) ) − ... + (1/(2019)) (((2018)),((2018)) ) h(x) is an odd function Then what is the value of ∫_(−3) ^( 3) f(x).g(x).h(x) dx ?

$$\mathrm{Given} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right)\:{dx}\:=\:\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{0}}\end{pmatrix}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{1}}\end{pmatrix}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{2}}\end{pmatrix}\:+\:...\:+\:\frac{\mathrm{1}}{\mathrm{2019}}\begin{pmatrix}{\mathrm{2018}}\\{\mathrm{2018}}\end{pmatrix} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:{g}\left({x}\right)\:{dx}\:=\:\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{0}}\end{pmatrix}\:−\:\frac{\mathrm{1}}{\mathrm{2}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{1}}\end{pmatrix}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{2}}\end{pmatrix}\:−\:...\:+\:\frac{\mathrm{1}}{\mathrm{2019}}\begin{pmatrix}{\mathrm{2018}}\\{\mathrm{2018}}\end{pmatrix} \\ $$$${h}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function} \\ $$$$\mathrm{Then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{−\mathrm{3}} ^{\:\mathrm{3}} \:{f}\left({x}\right).{g}\left({x}\right).{h}\left({x}\right)\:{dx}\:? \\ $$

Question Number 31141 Answers: 1 Comments: 0

using the limit defination find the area of f(x)= cos(x) [0,π/2]

$$\boldsymbol{{using}}\:\boldsymbol{{the}}\:\boldsymbol{{limit}}\:\boldsymbol{{defination}} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{area}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\:\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\:\:\left[\mathrm{0},\pi/\mathrm{2}\right] \\ $$

Pg 295 Pg 296 Pg 297 Pg 298 Pg 299 Pg 300 Pg 301 Pg 302 Pg 303 Pg 304

Terms of Service

Contact: info@tinkutara.com