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Question Number 64456 Answers: 0 Comments: 1

Question Number 64448 Answers: 1 Comments: 1

calculate lim_(x→π) ∫_(π/2) ^x (dx/(1+sinx−cosx))

$${calculate}\:{lim}_{{x}\rightarrow\pi} \:\:\int_{\frac{\pi}{\mathrm{2}}} ^{{x}} \:\:\:\frac{{dx}}{\mathrm{1}+{sinx}−{cosx}} \\ $$

Question Number 64447 Answers: 1 Comments: 0

Question Number 64445 Answers: 0 Comments: 0

calculate W_n =Σ_(1≤i≤j≤n) i×j

$${calculate}\:\:{W}_{{n}} =\sum_{\mathrm{1}\leqslant{i}\leqslant{j}\leqslant{n}} \:{i}×{j} \\ $$

Question Number 64444 Answers: 0 Comments: 2

calculate A_n =Σ_(k=0) ^n (k/((k+1)!))

$${calculate}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{{k}}{\left({k}+\mathrm{1}\right)!} \\ $$

Question Number 64443 Answers: 0 Comments: 0

find all functin f Z→Z wich verify ∀(a,b)∈Z^2 f(2a)+2f(b) =f(f(a+b))

$${find}\:{all}\:{functin}\:{f}\:{Z}\rightarrow{Z}\:\:{wich}\:{verify} \\ $$$$\forall\left({a},{b}\right)\in{Z}^{\mathrm{2}} \:\:\:\:\:{f}\left(\mathrm{2}{a}\right)+\mathrm{2}{f}\left({b}\right)\:={f}\left({f}\left({a}+{b}\right)\right) \\ $$

Question Number 64436 Answers: 2 Comments: 1

Question Number 64429 Answers: 0 Comments: 5

let f(x)=∫_0 ^1 (dt/(t+x+(√(t^2 +1)))) (x real parametre) 1) find a explicite form forf(x) 2)detemine also g(x) =∫_0 ^1 (dt/((t+x+(√(t^2 +1)))^2 )) 3)give f^((n)) (x) at form of integrals 4) find the values of ∫_0 ^1 (dt/(t+(√(t^2 +1)))) and ∫_0 ^1 (dt/((t+(√(t^2 +1)))^2 )) 5) find the values of ∫_0 ^1 (dt/(t+1 +(√(t^2 +1)))) and ∫_0 ^1 (dt/((t+1+(√(t^2 +1)))^2 ))

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{{t}+{x}+\sqrt{{t}^{\mathrm{2}} \:+\mathrm{1}}}\:\:\:\left({x}\:{real}\:{parametre}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicite}\:{form}\:{forf}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){detemine}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\left({t}+{x}+\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integrals} \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{{t}+\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}}\:\:{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\left({t}+\sqrt{{t}^{\mathrm{2}} \:+\mathrm{1}}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{5}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{{t}+\mathrm{1}\:+\sqrt{{t}^{\mathrm{2}} \:+\mathrm{1}}}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\left({t}+\mathrm{1}+\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{2}} } \\ $$

Question Number 64425 Answers: 0 Comments: 4

Question Number 64419 Answers: 0 Comments: 1

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

$$\left.\mathrm{1}\right)\:{find}\:\int\:\:\frac{{dx}}{{x}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{{x}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\ $$

Question Number 64418 Answers: 0 Comments: 3

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

$$\left.\mathrm{1}\right){find}\:\int\:\:\:\frac{{dx}}{{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$

Question Number 64414 Answers: 1 Comments: 0

The number of positive integers satisfying the inequality ^(n+1) C_(n−2) −^(n+1) C_(n−1) ≤ 100 is ____.

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{integers}\: \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{inequality}\: \\ $$$$\:^{{n}+\mathrm{1}} {C}_{{n}−\mathrm{2}} −\:^{{n}+\mathrm{1}} {C}_{{n}−\mathrm{1}} \leqslant\:\mathrm{100}\:\:\:\mathrm{is}\:\_\_\_\_. \\ $$

Question Number 64410 Answers: 1 Comments: 2

∫1/(1+ysinθ)dθ

$$\int\mathrm{1}/\left(\mathrm{1}+{ysin}\theta\right){d}\theta \\ $$

Question Number 64406 Answers: 0 Comments: 1

Question Number 64404 Answers: 0 Comments: 4

Question Number 64397 Answers: 1 Comments: 0

(7/(4x−1))−(5/(4x−1))

$$\frac{\mathrm{7}}{\mathrm{4x}−\mathrm{1}}−\frac{\mathrm{5}}{\mathrm{4x}−\mathrm{1}} \\ $$

Question Number 64396 Answers: 1 Comments: 0

(x+2)(x−2)

$$\left(\mathrm{x}+\mathrm{2}\right)\left(\mathrm{x}−\mathrm{2}\right) \\ $$

Question Number 64392 Answers: 0 Comments: 2

1)calculate A_n =∫_0 ^∞ ((sin(x^(2n) ))/((x^2 +1)^2 ))dx with n integr natural 2) study the convergene of Σ A_n

$$\left.\mathrm{1}\right){calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left({x}^{\mathrm{2}{n}} \right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergene}\:{of}\:\Sigma\:{A}_{{n}} \\ $$

Question Number 64391 Answers: 0 Comments: 1

(6/(a+5))+(4/(a+5))

$$\frac{\mathrm{6}}{\mathrm{a}+\mathrm{5}}+\frac{\mathrm{4}}{\mathrm{a}+\mathrm{5}} \\ $$

Question Number 64390 Answers: 1 Comments: 2

calculate ∫_1 ^(+∞) (dx/(x(√(4+x^2 ))))

$${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{dx}}{{x}\sqrt{\mathrm{4}+{x}^{\mathrm{2}} }} \\ $$

Question Number 64384 Answers: 1 Comments: 0

Question Number 64382 Answers: 1 Comments: 0

please help with workings ∫Ln[(√)(1−x)+(√)(1+x)]dx

$${please}\:\:{help}\:{with}\:{workings} \\ $$$$ \\ $$$$\int{Ln}\left[\sqrt{}\left(\mathrm{1}−{x}\right)+\sqrt{}\left(\mathrm{1}+{x}\right)\right]{dx} \\ $$

Question Number 64381 Answers: 0 Comments: 1

Question Number 64378 Answers: 0 Comments: 1

Question Number 64356 Answers: 1 Comments: 0

Question Number 64355 Answers: 0 Comments: 2

let F(x)=∫_(u(x)) ^(v(x{) f(x,t)dt how to calculate (dF/dx)(x)?

$${let}\:{F}\left({x}\right)=\int_{{u}\left({x}\right)} ^{{v}\left({x}\left\{\right.\right.} {f}\left({x},{t}\right){dt} \\ $$$${how}\:{to}\:{calculate}\:\:\frac{{dF}}{{dx}}\left({x}\right)? \\ $$

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