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Question Number 146835 Answers: 2 Comments: 0

calculate ∫_0 ^∞ (dx/((x^2 +3)^2 (x^2 +4)^2 ))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{2}} } \\ $$

Question Number 146824 Answers: 1 Comments: 0

Question Number 146868 Answers: 1 Comments: 0

if tan^2 x+sec x=a+1 has at least one solution then find the complete set of values of ′a′?

$${if}\:\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{sec}\:{x}={a}+\mathrm{1}\:{has}\:{at}\:{least}\: \\ $$$${one}\:{solution}\:{then}\:{find}\:{the}\:{complete}\:{set} \\ $$$${of}\:{values}\:{of}\:\:'{a}'? \\ $$

Question Number 146817 Answers: 1 Comments: 0

Question Number 146856 Answers: 0 Comments: 0

3. Calcula mediante una suma de Riemann una aproximaci´on al ´area limitada por la funci´on f(x) = −2x 2 − 4x + 30 y el eje x en el intervalo [−5, 3] con n rect´angulos. Δx=((3−(−5))/n) ⇒(8/n) ∴ x_0 =−5 ∴ a=x_0 =−5 x_1 =−5+1Δx x_2 =−5+2Δx x_3 =−5+3Δx ⋮ x_n =−5+nΔx

$$ \\ $$3. Calcula mediante una suma de Riemann una aproximaci´on al ´area limitada por la funci´on f(x) = −2x 2 − 4x + 30 y el eje x en el intervalo [−5, 3] con n rect´angulos. $$ \\ $$$$\Delta{x}=\frac{\mathrm{3}−\left(−\mathrm{5}\right)}{{n}}\:\Rightarrow\frac{\mathrm{8}}{{n}} \\ $$$$\therefore\:{x}_{\mathrm{0}} =−\mathrm{5} \\ $$$$ \\ $$$$\therefore\:{a}={x}_{\mathrm{0}} =−\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}_{\mathrm{1}} =−\mathrm{5}+\mathrm{1}\Delta{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}_{\mathrm{2}} =−\mathrm{5}+\mathrm{2}\Delta{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}_{\mathrm{3}} =−\mathrm{5}+\mathrm{3}\Delta{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\vdots \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{x}_{{n}} =−\mathrm{5}+{n}\Delta{x} \\ $$$$ \\ $$

Question Number 146799 Answers: 1 Comments: 0

Question Number 146791 Answers: 1 Comments: 0

∫(x/(1+cos^2 (x)))dx

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

Question Number 146790 Answers: 1 Comments: 0

∫(1/x) e^(−(1/x^2 )) dx

$$\int\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{e}^{−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} \mathrm{dx} \\ $$

Question Number 146784 Answers: 2 Comments: 2

Question Number 146782 Answers: 1 Comments: 0

Find the modulus of a complex number: Z = cos 40 + i sin 40 +1 = ?

$${Find}\:{the}\:{modulus}\:{of}\:{a}\:{complex} \\ $$$${number}: \\ $$$${Z}\:=\:{cos}\:\mathrm{40}\:+\:{i}\:{sin}\:\mathrm{40}\:+\mathrm{1}\:=\:? \\ $$

Question Number 146780 Answers: 1 Comments: 0

find by residue ∫_0 ^( 2π) (dθ/(1+ksinθ)) ,0<k<1

$${find}\:{by}\:{residue}\:\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \:\frac{{d}\theta}{\mathrm{1}+{ksin}\theta}\:\:\:,\mathrm{0}<{k}<\mathrm{1} \\ $$

Question Number 146778 Answers: 1 Comments: 0

Find the modulus of a complex number: Z = cos 40 + i sin 20 + 1 = ?

$${Find}\:{the}\:{modulus}\:{of}\:{a}\:{complex} \\ $$$${number}: \\ $$$${Z}\:=\:{cos}\:\mathrm{40}\:+\:{i}\:{sin}\:\mathrm{20}\:+\:\mathrm{1}\:=\:? \\ $$

Question Number 146776 Answers: 0 Comments: 2

Question Number 146775 Answers: 3 Comments: 0

Prove that ∫^( 𝛑) _( 0) tln(sint)dt= −(𝛑^2 /2)ln(2)

$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\:\:\underset{\:\mathrm{0}} {\int}^{\:\boldsymbol{\pi}} \boldsymbol{{tln}}\left(\boldsymbol{{sint}}\right)\boldsymbol{{dt}}=\:−\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{2}}\boldsymbol{{ln}}\left(\mathrm{2}\right) \\ $$

Question Number 146793 Answers: 1 Comments: 0

∀n≥2, u_n =Π_(k=2) ^n cos ((π/2^k )) et v_n =u_n sin ((π/2^n )) convergence, nature, sens of variations and adjantes? u_n and v_n help me please

$$\forall{n}\geqslant\mathrm{2},\:{u}_{{n}} =\underset{{k}=\mathrm{2}} {\overset{{n}} {\prod}}\mathrm{cos}\:\left(\frac{\pi}{\mathrm{2}^{{k}} }\right)\:{et}\:{v}_{{n}} ={u}_{{n}} \mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}^{{n}} }\right) \\ $$$${convergence},\:{nature},\:{sens}\:{of}\:{variations}\:{and}\:{adjantes}? \\ $$$${u}_{{n}} \:{and}\:{v}_{{n}} \\ $$$${help}\:{me}\:{please} \\ $$

Question Number 146772 Answers: 1 Comments: 0

If z=cos θ+i sin θ, prove that cos^6 θ=(1/(32))(cos 6θ+6cos 4θ+15cos 2θ+10). Hence or otherwise, find the value of ∫_0 ^( a) (√((a^2 −x^2 )^5 )) dx.

$$\mathrm{If}\:{z}=\mathrm{cos}\:\theta+{i}\:\mathrm{sin}\:\theta,\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{cos}^{\mathrm{6}} \theta=\frac{\mathrm{1}}{\mathrm{32}}\left(\mathrm{cos}\:\mathrm{6}\theta+\mathrm{6cos}\:\mathrm{4}\theta+\mathrm{15cos}\:\mathrm{2}\theta+\mathrm{10}\right). \\ $$$$\mathrm{Hence}\:\mathrm{or}\:\mathrm{otherwise},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:{a}} \sqrt{\left({a}^{\mathrm{2}} −{x}^{\mathrm{2}} \right)^{\mathrm{5}} }\:{dx}. \\ $$

Question Number 146771 Answers: 1 Comments: 0

Given that y′′−4y′+3y=0, y(0)=0, y′(0)=2, find y(ln 2).

$$\mathrm{Given}\:\mathrm{that}\:{y}''−\mathrm{4}{y}'+\mathrm{3}{y}=\mathrm{0},\:{y}\left(\mathrm{0}\right)=\mathrm{0},\:{y}'\left(\mathrm{0}\right)=\mathrm{2}, \\ $$$$\mathrm{find}\:{y}\left(\mathrm{ln}\:\mathrm{2}\right). \\ $$

Question Number 146767 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (((−1)^n )/(n+1))(1+(1/3)+...+(1/(2n+1)))=?

$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}+\mathrm{1}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+...+\frac{\mathrm{1}}{\mathrm{2n}+\mathrm{1}}\right)=? \\ $$

Question Number 146764 Answers: 0 Comments: 0

A=((((x+((2ax^2 ))^(1/3) )(2a+((2a^2 x))^(1/3) )^(−1) −1)/( (x)^(1/3) −((2a))^(1/3) ))−(2a)^(−1/3) )^(−6) , (a,b)∈R^2 a- A=((16a^4 )/x^2 ) b- A=(8/(ax)) c-A=(((2a))^(1/3) /(3x^3 ))

$$\mathrm{A}=\left(\frac{\left(\mathrm{x}+\sqrt[{\mathrm{3}}]{\mathrm{2ax}^{\mathrm{2}} }\right)\left(\mathrm{2a}+\sqrt[{\mathrm{3}}]{\mathrm{2a}^{\mathrm{2}} \mathrm{x}}\right)^{−\mathrm{1}} −\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{x}}−\sqrt[{\mathrm{3}}]{\mathrm{2a}}}−\left(\mathrm{2a}\right)^{−\mathrm{1}/\mathrm{3}} \right)^{−\mathrm{6}} ,\:\left(\mathrm{a},\mathrm{b}\right)\in\mathbb{R}^{\mathrm{2}} \\ $$$$\mathrm{a}-\:\mathrm{A}=\frac{\mathrm{16a}^{\mathrm{4}} }{\mathrm{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}-\:\mathrm{A}=\frac{\mathrm{8}}{\mathrm{ax}}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}-\mathrm{A}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{2a}}}{\mathrm{3x}^{\mathrm{3}} } \\ $$

Question Number 146761 Answers: 1 Comments: 1

Solve the partial defferintial equation u_t =a^2 u_(xx) ,0<x<L ,t>0 u(0,t)=0 and u(L,t)=0 and u_x (x,0)=f(x)

$${Solve}\:{the}\:{partial}\:{defferintial}\:{equation} \\ $$$${u}_{{t}} ={a}^{\mathrm{2}} {u}_{{xx}} \:\:\:,\mathrm{0}<{x}<{L}\:,{t}>\mathrm{0} \\ $$$$ \\ $$$${u}\left(\mathrm{0},{t}\right)=\mathrm{0}\:\:{and}\:{u}\left({L},{t}\right)=\mathrm{0}\:\:{and}\:{u}_{{x}} \left({x},\mathrm{0}\right)={f}\left({x}\right) \\ $$

Question Number 146758 Answers: 2 Comments: 0

find forier series to half rang of f(x)=sinx ,0<x<π and prove that Σ_(n=1) ^∞ (1/(4n^2 −1))=(1/2)

$${find}\:{forier}\:{series}\:{to}\:{half}\:{rang}\:{of}\: \\ $$$${f}\left({x}\right)={sinx}\:\:,\mathrm{0}<{x}<\pi\:{and}\:{prove}\:{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 146756 Answers: 2 Comments: 0

∫_( 0) ^( 1) t^2 + 1 dt

$$ \\ $$$$ \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:{t}^{\mathrm{2}} \:+\:\mathrm{1}\:{dt} \\ $$

Question Number 146755 Answers: 0 Comments: 0

lim_(p→+∞) Σ_(k=1) ^(p−1) (2/(k^2 (p−k)^2 ))=...?