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AllQuestion and Answers: Page 62

Question Number 215496 Answers: 1 Comments: 1

∫_0 ^π ((xtanx)/(secx + tanx)) dx Solve the integral.

$$\int_{\mathrm{0}} ^{\pi} \frac{{x}\mathrm{tan}{x}}{\mathrm{sec}{x}\:+\:\mathrm{tan}{x}}\:{dx} \\ $$$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{integral}. \\ $$

Question Number 215515 Answers: 0 Comments: 0

Question Number 215516 Answers: 1 Comments: 0

prove: Σ_(n=1) ^∞ (1/(π^2 n^2 +1))=(1/(e^2 −1))

$$\:\:\:\:\:\:\mathrm{prove}: \\ $$$$\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\pi^{\mathrm{2}} {n}^{\mathrm{2}} +\mathrm{1}}=\frac{\mathrm{1}}{{e}^{\mathrm{2}} −\mathrm{1}} \\ $$

Question Number 215492 Answers: 1 Comments: 1

Question Number 215572 Answers: 0 Comments: 1

Question Number 215473 Answers: 1 Comments: 0

Solve for x 2sin^2 x+3sin(x)+1=0 for 0 ≤ x

$${Solve}\:{for}\:{x} \\ $$$$ \\ $$$$\mathrm{2}{sin}^{\mathrm{2}} {x}+\mathrm{3}{sin}\left({x}\right)+\mathrm{1}=\mathrm{0}\:{for}\:\mathrm{0}\:\leqslant\:{x} \\ $$

Question Number 215528 Answers: 0 Comments: 2

Question Number 215469 Answers: 2 Comments: 0

Question Number 215468 Answers: 2 Comments: 0

((∂xω)/(∂yω))∙(∂e/∂ω)=? x=f(y) ω=g(y) e=h(ω)

$$\frac{\partial{x}\omega}{\partial{y}\omega}\centerdot\frac{\partial{e}}{\partial\omega}=? \\ $$$${x}={f}\left({y}\right) \\ $$$$\omega={g}\left({y}\right) \\ $$$${e}={h}\left(\omega\right) \\ $$

Question Number 215467 Answers: 0 Comments: 0

Question Number 215454 Answers: 1 Comments: 0

Question Number 215439 Answers: 2 Comments: 0

( 2 + (√2) )^8 = (√A) + (√B) Find: A−B = ?

$$\left(\:\mathrm{2}\:\:+\:\:\sqrt{\mathrm{2}}\:\right)^{\mathrm{8}} \:=\:\:\sqrt{\mathrm{A}}\:\:+\:\:\sqrt{\mathrm{B}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{A}−\mathrm{B}\:=\:? \\ $$

Question Number 215434 Answers: 0 Comments: 0

∫_0 ^( t) (√(t/(b−t))) e^t dt =?

$$\int_{\mathrm{0}} ^{\:\:{t}} \sqrt{\frac{{t}}{{b}−{t}}}\:{e}^{{t}} {dt}\:=? \\ $$

Question Number 215458 Answers: 1 Comments: 0

Evaluate lim_(n→∞) n^2 ∫_0 ^1 x^(n+1) sin(πx)dx

$$\mathrm{Evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}^{\mathrm{2}} \:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}+\mathrm{1}} \mathrm{sin}\left(\pi{x}\right){dx} \\ $$

Question Number 215418 Answers: 1 Comments: 0

Question Number 215417 Answers: 1 Comments: 0

a and b are complex numbers such that ∣b∣ = 1. Find ∣((b − a)/(1 − a^(−) b))∣

$${a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mid{b}\mid\:=\:\mathrm{1}.\:\mathrm{Find}\:\mid\frac{{b}\:−\:{a}}{\mathrm{1}\:−\:\overline {{a}b}}\mid \\ $$

Question Number 215414 Answers: 1 Comments: 2

∫ ((sin^3 ((x/2))sec((x/2)))/( (√(cos^3 x + cos^2 x + cosx)))) dx Solve this integral.

$$\int\:\frac{\mathrm{sin}^{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}}\right)\mathrm{sec}\left(\frac{{x}}{\mathrm{2}}\right)}{\:\sqrt{\mathrm{cos}^{\mathrm{3}} {x}\:+\:\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{cos}{x}}}\:{dx} \\ $$$$\mathrm{Solve}\:\mathrm{this}\:\mathrm{integral}. \\ $$

Question Number 215445 Answers: 3 Comments: 0

Question Number 215404 Answers: 1 Comments: 0

∫_a ^( x) ((√(1+4x^2 ))/( (√(a^2 −x^2 ))))dx = ?

$$\int_{{a}} ^{\:\:{x}} \:\frac{\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }}{\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }}{dx}\:=\:? \\ $$

Question Number 215400 Answers: 3 Comments: 1

Question Number 215393 Answers: 0 Comments: 1

∫_0 ^∞ (x^(2ν) /((x^2 +β^2 )^(μ+1) ))sin(ax)dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{2}\nu} }{\left({x}^{\mathrm{2}} +\beta^{\mathrm{2}} \right)^{\mu+\mathrm{1}} }\mathrm{sin}\left({ax}\right){dx} \\ $$$$ \\ $$

Question Number 215386 Answers: 1 Comments: 0

Question Number 215372 Answers: 1 Comments: 0

Question Number 215390 Answers: 1 Comments: 0

∮_γ x^2 dx [γ: x^2 +y^2 =1]

$$\oint_{\gamma} {x}^{\mathrm{2}} {dx}\:\left[\gamma:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right] \\ $$

Question Number 215356 Answers: 1 Comments: 0

Solve: x^2 =a+(y−z)^2 y^2 =b+(z−x)^2 z^2 =c+(x−y)^2

$$\:{Solve}: \\ $$$$\:\:{x}^{\mathrm{2}} ={a}+\left({y}−{z}\right)^{\mathrm{2}} \\ $$$$\:\:{y}^{\mathrm{2}} ={b}+\left({z}−{x}\right)^{\mathrm{2}} \\ $$$$\:\:{z}^{\mathrm{2}} ={c}+\left({x}−{y}\right)^{\mathrm{2}} \\ $$

Question Number 215350 Answers: 2 Comments: 0

Find: x^x = 2^(√(200)) ⇒ x = ?

$$\mathrm{Find}:\:\:\:\mathrm{x}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{2}^{\sqrt{\mathrm{200}}} \:\:\Rightarrow\:\:\mathrm{x}\:=\:? \\ $$

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