Question and Answers Forum

IntegrationQuestion and Answers: Page 25

Question Number 187700 Answers: 0 Comments: 1

Find minimum area of the part y=x^2 and y=kx(x^2 −k), k>0

$$\:{Find}\:{minimum}\:{area}\:{of}\:{the}\:{part} \\ $$$$\:{y}={x}^{\mathrm{2}} \:{and}\:{y}={kx}\left({x}^{\mathrm{2}} −{k}\right),\:{k}>\mathrm{0}\: \\ $$

Question Number 187602 Answers: 1 Comments: 0

∫_(1/4) ^(1/2) ((sin^(−1) ((√x))−cos^(−1) ((√x)))/(sin^(−1) ((√x))+cos^(−1) ((√x)))) dx=?

$$\:\:\:\underset{\mathrm{1}/\mathrm{4}} {\overset{\mathrm{1}/\mathrm{2}} {\int}}\:\frac{\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{{x}}\right)−\mathrm{cos}^{−\mathrm{1}} \left(\sqrt{{x}}\right)}{\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{{x}}\right)+\mathrm{cos}^{−\mathrm{1}} \left(\sqrt{{x}}\right)}\:{dx}=? \\ $$

Question Number 187531 Answers: 3 Comments: 0

∫_0 ^∞ x^2 e^(−x) dx=?

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}{x}^{\mathrm{2}} {e}^{−{x}} {dx}=? \\ $$

Question Number 187530 Answers: 1 Comments: 0

∫(dx/( (√(a^2 +be^(cx) ))))=?

$$\int\frac{{dx}}{\:\sqrt{{a}^{\mathrm{2}} +{be}^{{cx}} }}=? \\ $$

Question Number 187529 Answers: 1 Comments: 0

∫x^2 ∙sin^(−1) (x)dx=?

$$\int{x}^{\mathrm{2}} \centerdot{sin}^{−\mathrm{1}} \left({x}\right){dx}=? \\ $$

Question Number 187528 Answers: 1 Comments: 0

∫_((9π)/2) ^((7π)/(1.5)) (dx/( (√(1−sinx))))=?

$$\underset{\frac{\mathrm{9}\pi}{\mathrm{2}}} {\overset{\frac{\mathrm{7}\pi}{\mathrm{1}.\mathrm{5}}} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{1}−{sinx}}}=? \\ $$

Question Number 187526 Answers: 2 Comments: 0

∫(dx/(cscx−1))=?

$$\int\frac{{dx}}{{cscx}−\mathrm{1}}=? \\ $$

Question Number 187374 Answers: 0 Comments: 2

∫(√((t+1)/(t(k−t))))dt=?

$$\int\sqrt{\frac{{t}+\mathrm{1}}{{t}\left({k}−{t}\right)}}{dt}=? \\ $$

Question Number 187317 Answers: 2 Comments: 0

∫(dx/(x(√(1−2x))))

$$\int\frac{{dx}}{{x}\sqrt{\mathrm{1}−\mathrm{2}{x}}} \\ $$

Question Number 187251 Answers: 0 Comments: 1

∫ ((cos 9x)/(cos 4x. cos 2x)) dx=?

$$\:\:\int\:\frac{\mathrm{cos}\:\mathrm{9}{x}}{\mathrm{cos}\:\mathrm{4}{x}.\:\mathrm{cos}\:\mathrm{2}{x}}\:{dx}=? \\ $$

Question Number 187164 Answers: 1 Comments: 0

Question Number 187135 Answers: 1 Comments: 0

∫_( 0) ^( π/4) ((tan^2 x)/(1+sin x)) dx =?

$$\:\underset{\:\:\mathrm{0}} {\overset{\:\:\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{tan}\:^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx}\:=? \\ $$

Question Number 187095 Answers: 2 Comments: 1

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

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

Question Number 187050 Answers: 0 Comments: 1

∫^(𝛑/4) _0 ((cos^(−1) x + cos x)/(Ln x)) dx =??

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\int}^{\frac{\boldsymbol{\pi}}{\mathrm{4}}} \:\:\frac{\boldsymbol{{cos}}^{−\mathrm{1}} \boldsymbol{{x}}\:+\:\boldsymbol{{cos}}\:\boldsymbol{{x}}}{\boldsymbol{{Ln}}\:\boldsymbol{{x}}}\:\:\boldsymbol{{dx}}\:=??\:\:\: \\ $$$$ \\ $$

Question Number 186921 Answers: 0 Comments: 0

Question Number 186911 Answers: 1 Comments: 0

∫_0 ^∞ (1/(1+a^x +a^(x/2) ))dx = (1/(ln a))[ln 3−(π/(3(√3)))]

$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\mathrm{1}+{a}^{{x}} +{a}^{\frac{{x}}{\mathrm{2}}} }{dx}\:=\:\frac{\mathrm{1}}{\mathrm{ln}\:{a}}\left[\mathrm{ln}\:\mathrm{3}−\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}}\right] \\ $$

Question Number 186910 Answers: 1 Comments: 0

∫_0 ^a (√((cos 2x−cos 2a)/(cos 2x+1))) dx=(π/2)(1−cos a)

$$ \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{{a}} \sqrt{\frac{\mathrm{cos}\:\mathrm{2}{x}−\mathrm{cos}\:\mathrm{2}{a}}{\mathrm{cos}\:\mathrm{2}{x}+\mathrm{1}}}\:{dx}=\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\mathrm{cos}\:{a}\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 186973 Answers: 0 Comments: 1

∫5x

$$\int\mathrm{5}{x} \\ $$

Question Number 186856 Answers: 0 Comments: 0

∫ (((√(x+3))+(√(x+2)))/( (√(x+3))+(√(x−2)))) dx =?

$$\int\:\frac{\sqrt{{x}+\mathrm{3}}+\sqrt{{x}+\mathrm{2}}}{\:\sqrt{{x}+\mathrm{3}}+\sqrt{{x}−\mathrm{2}}}\:{dx}\:=? \\ $$

Question Number 186840 Answers: 1 Comments: 0

∫_9 ^( 16) ((√(4−(√x)))/x) dx =?

$$\:\:\underset{\mathrm{9}} {\overset{\:\mathrm{16}} {\int}}\:\frac{\sqrt{\mathrm{4}−\sqrt{{x}}}}{{x}}\:{dx}\:=? \\ $$

Question Number 186800 Answers: 0 Comments: 0

show that ∫_0 ^( ∞ ) ((tan^(−1) 𝛂x tan^(−1) 𝛃x)/x^2 )dx = (𝛑/2)log{(((𝛂+𝛃)^(𝛂+𝛃) )/(𝛂^𝛂 𝛃^𝛃 ))}

$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\:\infty\:} \frac{\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \boldsymbol{\alpha{x}}\:\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \boldsymbol{\beta{x}}}{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}\:=\:\frac{\boldsymbol{\pi}}{\mathrm{2}}\mathrm{log}\left\{\frac{\left(\boldsymbol{\alpha}+\boldsymbol{\beta}\right)^{\boldsymbol{\alpha}+\boldsymbol{\beta}} }{\boldsymbol{\alpha}^{\boldsymbol{\alpha}} \boldsymbol{\beta}^{\boldsymbol{\beta}} }\right\}\: \\ $$

Question Number 186771 Answers: 2 Comments: 0

Q : Find the value of the following integral. I = ∫_0 ^( (( π)/( 2))) (( 1)/( 1 + sin^( 4) ( x ) + cos^( 4) ( x ) )) dx = ?

$$ \\ $$$$\:\:\:\:\mathrm{Q}\::\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{integral}.\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\frac{\:\pi}{\:\mathrm{2}}} \:\frac{\:\:\mathrm{1}}{\:\mathrm{1}\:+\:\mathrm{sin}^{\:\mathrm{4}} \:\left(\:{x}\:\right)\:+\:\mathrm{cos}^{\:\mathrm{4}} \:\left(\:{x}\:\right)\:}\:\mathrm{d}{x}\:=\:\:?\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 186780 Answers: 1 Comments: 0

∫ ((1 + sin x + cos x)/(1 + sin x)) dx

$$ \\ $$$$\:\:\:\:\:\:\:\int\:\:\:\frac{\mathrm{1}\:+\:\boldsymbol{{sin}}\:\boldsymbol{{x}}\:+\:\boldsymbol{{cos}}\:\boldsymbol{{x}}}{\mathrm{1}\:+\:\boldsymbol{{sin}}\:\boldsymbol{{x}}}\:\:\boldsymbol{{dx}}\:\: \\ $$$$ \\ $$

Question Number 186736 Answers: 1 Comments: 0

Question Number 186735 Answers: 1 Comments: 0

Question Number 186726 Answers: 2 Comments: 0

Pg 20 Pg 21 Pg 22 Pg 23 Pg 24 Pg 25 Pg 26 Pg 27 Pg 28 Pg 29

Contact: info@tinkutara.com