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IntegrationQuestion and Answers: Page 263

Question Number 46188 Answers: 0 Comments: 5

Using dimensional analysis , find out value of n in given expression: ∫(dx/(√(2ax−x^2 ))) = a^n sin^(−1) ((x/a) −1).

$${Using}\:{dimensional}\:{analysis}\:, \\ $$$${find}\:{out}\:{value}\:{of}\:{n}\:{in}\:{given}\:{expression}: \\ $$$$\:\:\int\frac{{dx}}{\sqrt{\mathrm{2}{ax}−{x}^{\mathrm{2}} }}\:=\:{a}^{{n}} \mathrm{sin}^{−\mathrm{1}} \left(\frac{{x}}{{a}}\:−\mathrm{1}\right). \\ $$

Question Number 46182 Answers: 1 Comments: 4

Question Number 46171 Answers: 0 Comments: 1

find ∫ (dx/((√x)+(√(x+1)) +(√(x+2))))

$${find}\:\int\:\:\:\:\frac{{dx}}{\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\:+\sqrt{{x}+\mathrm{2}}} \\ $$

Question Number 46156 Answers: 1 Comments: 0

Question Number 46129 Answers: 0 Comments: 4

Question Number 46103 Answers: 1 Comments: 3

Find the area enclosed between curves y^2 (2a−x)=x^3 and line x=2 above the x−axis ? Graphing calculators are not allowed..

$${Find}\:{the}\:{area}\:{enclosed}\:{between}\:{curves} \\ $$$${y}^{\mathrm{2}} \left(\mathrm{2}{a}−{x}\right)={x}^{\mathrm{3}} \:{and}\:{line}\:{x}=\mathrm{2}\:{above}\:{the} \\ $$$${x}−{axis}\:? \\ $$$${Graphing}\:{calculators}\:{are}\:{not}\:{allowed}.. \\ $$

Question Number 46101 Answers: 1 Comments: 0

I=∫(x^(n+1) /(√(1+x^n )))dx=?

$$\mathrm{I}=\int\frac{\mathrm{x}^{\mathrm{n}+\mathrm{1}} }{\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{n}} }}\mathrm{dx}=? \\ $$

Question Number 46091 Answers: 1 Comments: 1

Question Number 46087 Answers: 1 Comments: 0

please help me!! calculate: I=∫_2 ^(1+e^2 ) ((12288ln(x−1))/([ln^(12) (x−1)+4096](x−1)))dx thanks!!!

$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}!! \\ $$$$\mathrm{calculate}: \\ $$$$\mathrm{I}=\underset{\mathrm{2}} {\overset{\mathrm{1}+\mathrm{e}^{\mathrm{2}} } {\int}}\frac{\mathrm{12288ln}\left(\mathrm{x}−\mathrm{1}\right)}{\left[\mathrm{ln}^{\mathrm{12}} \left(\mathrm{x}−\mathrm{1}\right)+\mathrm{4096}\right]\left(\mathrm{x}−\mathrm{1}\right)}\mathrm{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{thanks}!!! \\ $$

Question Number 46014 Answers: 0 Comments: 0

Question Number 45975 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(1+t^2 ))/(1+t^2 ))dt

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 45973 Answers: 0 Comments: 0

find ∫ sh(x)ln(x+(√(1+x^2 )))dx

$${find}\:\int\:\:{sh}\left({x}\right){ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right){dx} \\ $$

Question Number 45972 Answers: 0 Comments: 0

find ∫ ch(x)ln(x+(√(x^2 −1)))dx

$${find}\:\:\int\:\:{ch}\left({x}\right){ln}\left({x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\right){dx} \\ $$

Question Number 45971 Answers: 0 Comments: 0

calculate f(x)=∫_0 ^1 ((arctan(xt))/(1+x^2 t^2 ))dt

$${calculate}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{arctan}\left({xt}\right)}{\mathrm{1}+{x}^{\mathrm{2}} {t}^{\mathrm{2}} }{dt} \\ $$

Question Number 45970 Answers: 1 Comments: 1

find ∫ ((arcsin(2x))/(√(1−4x^2 )))dx

$${find}\:\int\:\:\frac{{arcsin}\left(\mathrm{2}{x}\right)}{\sqrt{\mathrm{1}−\mathrm{4}{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 45969 Answers: 0 Comments: 0

1) find f(x)=∫_0 ^1 ln(1+ix)dx 2) calculate f^′ (x)

$$\left.\mathrm{1}\right)\:{find}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{ix}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$

Question Number 45916 Answers: 1 Comments: 0

∫f(x)dx=f(×)+c

$$\int{f}\left({x}\right){dx}={f}\left(×\right)+{c} \\ $$

Question Number 45885 Answers: 1 Comments: 3

Question Number 45841 Answers: 1 Comments: 2

∫_0 ^( ∞) e^(−ix^2 ) dx=?? plz..

$$\int_{\mathrm{0}} ^{\:\infty} \:{e}^{−{ix}^{\mathrm{2}} } {dx}=?? \\ $$$$\mathrm{plz}.. \\ $$

Question Number 45836 Answers: 0 Comments: 3

∫(1/(sin^2 x))∙(1/((3+2cosx)))dx=?

$$\int\frac{\mathrm{1}}{{sin}^{\mathrm{2}} {x}}\centerdot\frac{\mathrm{1}}{\left(\mathrm{3}+\mathrm{2}{cosx}\right)}{dx}=? \\ $$

Question Number 45802 Answers: 0 Comments: 1

some practice for the brave... ∫((cos^2 x sin^2 x)/(cos x +sin x))dx=? ∫((cos^2 x tan^2 x)/(cos x +tan x))dx=? ∫((sin^2 x tan^2 x)/(sin x +tan x))dx=?

$$\mathrm{some}\:\mathrm{practice}\:\mathrm{for}\:\mathrm{the}\:\mathrm{brave}... \\ $$$$\int\frac{\mathrm{cos}^{\mathrm{2}} \:{x}\:\mathrm{sin}^{\mathrm{2}} \:{x}}{\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}}{dx}=? \\ $$$$\int\frac{\mathrm{cos}^{\mathrm{2}} \:{x}\:\mathrm{tan}^{\mathrm{2}} \:{x}}{\mathrm{cos}\:{x}\:+\mathrm{tan}\:{x}}{dx}=? \\ $$$$\int\frac{\mathrm{sin}^{\mathrm{2}} \:{x}\:\mathrm{tan}^{\mathrm{2}} \:{x}}{\mathrm{sin}\:{x}\:+\mathrm{tan}\:{x}}{dx}=? \\ $$

Question Number 45795 Answers: 1 Comments: 0

find ∫ (dx/(cosx sin^2 x))

$${find}\:\int\:\frac{{dx}}{{cosx}\:{sin}^{\mathrm{2}} {x}} \\ $$

Question Number 45771 Answers: 1 Comments: 0

find f(x)=∫_0 ^∞ cos(x+t^2 )dtand g(x)=∫_0 ^∞ sin(x+t^2 )dt 2) find the value of f^′ (x) and g^′ (x).

$${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}+{t}^{\mathrm{2}} \right){dtand}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}+{t}^{\mathrm{2}} \right){dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{f}^{'} \left({x}\right)\:{and}\:{g}^{'} \left({x}\right). \\ $$

Question Number 45735 Answers: 2 Comments: 1

∫_α ^β (1/((x−α)(β−x)))dx =? β>α

$$\int_{\alpha} ^{\beta} \frac{\mathrm{1}}{\left({x}−\alpha\right)\left(\beta−{x}\right)}{dx}\:\:=?\:\:\:\beta>\alpha \\ $$

Question Number 45721 Answers: 0 Comments: 3

Integrate sin (x^2 )dx

$$\:{Integrate}\:\mathrm{sin}\:\left({x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 45706 Answers: 1 Comments: 0

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