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IntegrationQuestion and Answers: Page 187

Question Number 88170 Answers: 0 Comments: 2

Prove that ∫_0 ^1 tcos nπtdt=(((−1)^n −1)/(n^2 π^2 ))

$${Prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {tcos}\:{n}\pi{tdt}=\frac{\left(−\mathrm{1}\right)^{{n}} −\mathrm{1}}{{n}^{\mathrm{2}} \pi^{\mathrm{2}} } \\ $$

Question Number 88153 Answers: 0 Comments: 1

Question Number 88131 Answers: 1 Comments: 0

∫((x^2 +1)/(x−(√(1−2x))))dx

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

Question Number 88118 Answers: 1 Comments: 1

∫(dx/((x+1)×(√x)))

$$\int\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)×\sqrt{\mathrm{x}}} \\ $$

Question Number 88104 Answers: 1 Comments: 2

∫_0 ^(+∞) (√(3+e^(−2x) ))dx

$$\int_{\mathrm{0}} ^{+\infty} \sqrt{\mathrm{3}+{e}^{−\mathrm{2}{x}} }{dx} \\ $$

Question Number 88097 Answers: 1 Comments: 0

∫(dx/((2x−3)^(2/3) ))

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

Question Number 88089 Answers: 1 Comments: 1

∫(e^x /(e^2 −9))dx

$$\int\frac{{e}^{{x}} }{{e}^{\mathrm{2}} −\mathrm{9}}{dx} \\ $$

Question Number 88071 Answers: 1 Comments: 7

Question Number 88069 Answers: 1 Comments: 2

Question Number 88064 Answers: 1 Comments: 0

∫ (dx/(cos x(2+sin x)))?

$$\int\:\frac{\mathrm{dx}}{\mathrm{cos}\:\mathrm{x}\left(\mathrm{2}+\mathrm{sin}\:\mathrm{x}\right)}? \\ $$

Question Number 88045 Answers: 0 Comments: 2

∫ ((sin x)/(2sin x+cos x)) dx

$$\int\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{2sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$

Question Number 88042 Answers: 1 Comments: 0

find max and min value of function f(x) = (5/(−3cos x−4sin x))

$$\mathrm{find}\:\mathrm{max}\:\mathrm{and}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{5}}{−\mathrm{3cos}\:\mathrm{x}−\mathrm{4sin}\:\mathrm{x}} \\ $$

Question Number 88033 Answers: 0 Comments: 4

find ∫_0 ^1 ((sin(x))/x)dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sin}\left({x}\right)}{{x}}{dx} \\ $$

Question Number 88026 Answers: 0 Comments: 0

Question Number 88010 Answers: 0 Comments: 2

∫((x^2 +2x+3)/(√(x^2 +x+1)))dx

$$\int\frac{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}}{\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$

Question Number 88007 Answers: 1 Comments: 0

∫_0 ^1 (√((√((4/x)−3))−1))dx=?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\sqrt{\sqrt{\frac{\mathrm{4}}{{x}}−\mathrm{3}}−\mathrm{1}}{dx}=? \\ $$

Question Number 88003 Answers: 0 Comments: 2

Determine all functions f[0,1]→Ω such that ∀x∈[0,1] f ′(x)+f(x)=f(0)+f(1)

$${Determine}\:{all}\:{functions}\:{f}\left[\mathrm{0},\mathrm{1}\right]\rightarrow\Omega \\ $$$${such}\:{that}\:\forall{x}\in\left[\mathrm{0},\mathrm{1}\right]\:{f}\:'\left({x}\right)+{f}\left({x}\right)={f}\left(\mathrm{0}\right)+{f}\left(\mathrm{1}\right) \\ $$

Question Number 87996 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(3x)−arctanx)/x)dx

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

Question Number 87995 Answers: 1 Comments: 0

find ∫ (dx/((x^2 −1)^2 (x^2 +2)))

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

Question Number 87994 Answers: 0 Comments: 0

vcalculate ∫_0 ^∞ ((arctan(2[x]+3))/(x^2 +9))dx

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

Question Number 87993 Answers: 0 Comments: 1

calculate ∫_0 ^∞ (dx/((x+1)^2 (x+2)^2 (x+3)^2 ))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({x}+\mathrm{2}\right)^{\mathrm{2}} \left({x}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 87977 Answers: 0 Comments: 2

∫_(−(π/2)) ^(π/2) ((sin 2x)/(1+2^x ))dx

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

Question Number 87969 Answers: 1 Comments: 0

Question Number 87930 Answers: 0 Comments: 0

Question Number 87920 Answers: 0 Comments: 1

Question Number 87910 Answers: 0 Comments: 0

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