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let f(x) =∫_0 ^1 (dt/(1+xch(t))) with x real 1) determine a explicit form of f(x) 2)find also g(x)=∫_0 ^1 (dt/((1+xch(t))^2 )) 3) calculate ∫_0 ^1 (dt/(1+3ch(t))) and ∫_0 ^1 (dt/((1+3ch(t))^2 ))

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{1}+{xch}\left({t}\right)}\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{\left(\mathrm{1}+{xch}\left({t}\right)\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{1}+\mathrm{3}{ch}\left({t}\right)}\:{and}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+\mathrm{3}{ch}\left({t}\right)\right)^{\mathrm{2}} } \\ $$

Question Number 59526 Answers: 1 Comments: 1

calculate ∫_0 ^1 (dx/(2sh(x)+3ch(x)))

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

Question Number 59518 Answers: 1 Comments: 1

if x+y+z=1 x^2 +y^2 +z^2 =2 x^3 +y^3 +z^3 =3 calculste x^5 +y^5 +z^5

$${if}\:\:{x}+{y}+{z}=\mathrm{1} \\ $$$${x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}^{\mathrm{3}} \:+{y}^{\mathrm{3}} \:+{z}^{\mathrm{3}} =\mathrm{3}\:\:{calculste} \\ $$$${x}^{\mathrm{5}} +{y}^{\mathrm{5}} \:+{z}^{\mathrm{5}} \\ $$

Question Number 59516 Answers: 1 Comments: 0

Question Number 59515 Answers: 0 Comments: 0

Question Number 59509 Answers: 2 Comments: 0

Question Number 59506 Answers: 1 Comments: 4

Question Number 59505 Answers: 2 Comments: 0

Two particles P and Q move towards each other along a straight line MN, 51 meters long. P starts fromM with velocity 5 ms^(−1) and constant acceleration of 1 ms^(−2) . Q starts from N at the same time with velocity 6 ms^(−1) and at a constant acceleration of 3 ms^(−2) . Find the time when the: (a) particles are 30 metres apart; (b) particles meet; (c) velocity of P is (3/4) os the velocity of Q.

$$\mathrm{Two}\:\mathrm{particles}\:\mathrm{P}\:\mathrm{and}\:\mathrm{Q}\:\mathrm{move}\:\mathrm{towards}\:\mathrm{each} \\ $$$$\mathrm{other}\:\mathrm{along}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:{MN},\:\mathrm{51}\:\mathrm{meters} \\ $$$$\mathrm{long}.\:\mathrm{P}\:\mathrm{starts}\:\mathrm{from}{M}\:\mathrm{with}\:\mathrm{velocity}\:\mathrm{5}\:\mathrm{ms}^{−\mathrm{1}} \\ $$$$\mathrm{and}\:\mathrm{constant}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{1}\:\mathrm{ms}^{−\mathrm{2}} .\:\mathrm{Q}\:\mathrm{starts} \\ $$$$\mathrm{from}\:\mathrm{N}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{time}\:\mathrm{with}\:\mathrm{velocity}\:\mathrm{6}\:\mathrm{ms}^{−\mathrm{1}} \\ $$$$\mathrm{and}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{3}\:\mathrm{ms}^{−\mathrm{2}} . \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{time}\:\mathrm{when}\:\mathrm{the}: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{particles}\:\mathrm{are}\:\mathrm{30}\:\mathrm{metres}\:\mathrm{apart}; \\ $$$$\left(\mathrm{b}\right)\:\mathrm{particles}\:\mathrm{meet}; \\ $$$$\left(\mathrm{c}\right)\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{P}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{os}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{Q}. \\ $$

Question Number 59503 Answers: 0 Comments: 1

∫_a ^b (e^(−x^2 ) )dx=?

$$\underset{\boldsymbol{{a}}} {\overset{\boldsymbol{{b}}} {\int}}\left(\boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } \right)\boldsymbol{{dx}}=? \\ $$

Question Number 59499 Answers: 1 Comments: 3