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Question Number 62145 Answers: 1 Comments: 1

calculate ∫_0 ^π ln(x^2 −2xsinθ +1)dθ

$${calculate}\:\:\int_{\mathrm{0}} ^{\pi} {ln}\left({x}^{\mathrm{2}} −\mathrm{2}{xsin}\theta\:+\mathrm{1}\right){d}\theta \\ $$

Question Number 62142 Answers: 0 Comments: 0

6.38÷0.2

$$\mathrm{6}.\mathrm{38}\boldsymbol{\div}\mathrm{0}.\mathrm{2} \\ $$

Question Number 62141 Answers: 0 Comments: 1

let A =∫_0 ^(+∞) (dx/((x^2 −i)^2 )) ( i^2 =−1) 1) calculate A 2) let R =Re(A) and I =Im(A) find the value of R and I .

$${let}\:{A}\:=\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:−{i}\right)^{\mathrm{2}} }\:\:\:\:\:\left(\:{i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{R}\:={Re}\left({A}\right)\:{and}\:{I}\:={Im}\left({A}\right) \\ $$$${find}\:\:{the}\:{value}\:{of}\:{R}\:{and}\:{I}\:. \\ $$

Question Number 62140 Answers: 1 Comments: 0

2÷(1/3)

$$\mathrm{2}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{3}} \\ $$

Question Number 62139 Answers: 0 Comments: 0

6+5>3×5 true or false

$$\mathrm{6}+\mathrm{5}>\mathrm{3}×\mathrm{5}\:\mathrm{true}\:\mathrm{or}\:\mathrm{false} \\ $$

Question Number 62138 Answers: 0 Comments: 0

5^1

$$\mathrm{5}^{\mathrm{1}} \\ $$

Question Number 62137 Answers: 0 Comments: 0

((1/4))^3

$$\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{3}} \\ $$

Question Number 62136 Answers: 0 Comments: 0

3 of (1/6)

$$\mathrm{3}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{6}} \\ $$

Question Number 62135 Answers: 0 Comments: 0

(√(100))

$$\sqrt{\mathrm{100}} \\ $$

Question Number 62134 Answers: 0 Comments: 0

8^4 ×8^2

$$\mathrm{8}^{\mathrm{4}} ×\mathrm{8}^{\mathrm{2}} \\ $$

Question Number 62133 Answers: 0 Comments: 0

5(2+3+1)

$$\mathrm{5}\left(\mathrm{2}+\mathrm{3}+\mathrm{1}\right) \\ $$

Question Number 62132 Answers: 0 Comments: 0

(3×2)^2

$$\left(\mathrm{3}×\mathrm{2}\right)^{\mathrm{2}} \\ $$

Question Number 62131 Answers: 0 Comments: 0

(1/3)+3(1/4)

$$\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{3}\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 62130 Answers: 1 Comments: 0

(√(α^2 −β^2 )) simplify

$$\sqrt{\alpha^{\mathrm{2}} −\beta^{\mathrm{2}} } \\ $$$${simplify}\: \\ $$$$ \\ $$

Question Number 62129 Answers: 0 Comments: 4

let f(x)=ln(x+1−2(√x)) 1) find D_f 2) determine f^(−1) 3) calculate ∫f (x)dx and ∫ f^(−1) (x)dx

$${let}\:{f}\left({x}\right)={ln}\left({x}+\mathrm{1}−\mathrm{2}\sqrt{{x}}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{f}^{−\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int{f}\:\left({x}\right){dx}\:{and}\:\:\int\:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$

Question Number 62128 Answers: 0 Comments: 3

let U_n = ∫_0 ^∞ ((cos(nx))/((x^2 +n^2 )^3 ))dx with n≥1 1) calculate U_n intrems of n 2) find lim_(n→+∞) n U_n 3) calculate lim_(n→+∞) n^2 U_n 4) study the convervence of U_n

$${let}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} \right)^{\mathrm{3}} }{dx}\:\:{with}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{intrems}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {n}\:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} {n}^{\mathrm{2}} \:{U}_{{n}} \\ $$$$\left.\mathrm{4}\right)\:{study}\:{the}\:{convervence}\:{of}\:{U}_{{n}} \\ $$

Question Number 62124 Answers: 0 Comments: 0

Question Number 62122 Answers: 0 Comments: 4

∫e^(cos(x)) sin(sin(x)) dx

$$\int{e}^{{cos}\left({x}\right)} {sin}\left({sin}\left({x}\right)\right)\:{dx}\: \\ $$

Question Number 62121 Answers: 2 Comments: 0

A cube of unit edge length is held before a plane. Prove that the sum of the squares of the projected lengths of edges of the cube on the plane (irrespective of the orientation of the cube) is 8.

$${A}\:{cube}\:{of}\:{unit}\:{edge}\:{length}\: \\ $$$${is}\:{held}\:{before}\:{a}\:{plane}.\:{Prove}\:{that} \\ $$$${the}\:{sum}\:{of}\:{the}\:{squares}\:{of}\:{the} \\ $$$${projected}\:{lengths}\:{of}\:{edges}\:{of}\:{the}\:{cube} \\ $$$${on}\:{the}\:{plane}\:\left({irrespective}\:{of}\right. \\ $$$$\left.{the}\:{orientation}\:{of}\:{the}\:{cube}\right)\:{is}\:\mathrm{8}. \\ $$

Question Number 62112 Answers: 2 Comments: 0

Question Number 62109 Answers: 1 Comments: 2

Given that (1+(√(1+x)))tan x=(1+(√(1−x))). Then find sin 4x.

$${Given}\:{that} \\ $$$$\left(\mathrm{1}+\sqrt{\mathrm{1}+{x}}\right)\mathrm{tan}\:{x}=\left(\mathrm{1}+\sqrt{\mathrm{1}−{x}}\right). \\ $$$${Then}\:{find}\:\:\:\mathrm{sin}\:\mathrm{4}{x}. \\ $$

Question Number 62102 Answers: 1 Comments: 0

Question Number 62096 Answers: 0 Comments: 0

Question Number 62094 Answers: 0 Comments: 2

Question Number 62093 Answers: 0 Comments: 1

∫ (dx/(sin^3 x + cos^3 x)) = p

$$\int\:\:\frac{{dx}}{\mathrm{sin}^{\mathrm{3}} \:{x}\:+\:\mathrm{cos}^{\mathrm{3}} \:{x}}\:\:=\:\:{p} \\ $$

Question Number 62092 Answers: 0 Comments: 1

MATH MEME: 3+x = 1+8 :) ((3+x)/+) = ((1+8)/+) cancel the plus sign 3x = 18 ((3x)/3) = ((18)/3) x = 6 am i correct?

$$\mathrm{MATH}\:\mathrm{MEME}: \\ $$$$\mathrm{3}+\mathrm{x}\:=\:\mathrm{1}+\mathrm{8} \\ $$$$\left.:\right) \\ $$$$\frac{\mathrm{3}+\mathrm{x}}{+}\:=\:\frac{\mathrm{1}+\mathrm{8}}{+} \\ $$$${cancel}\:{the}\:{plus}\:{sign} \\ $$$$\mathrm{3}{x}\:=\:\mathrm{18} \\ $$$$\frac{\mathrm{3}{x}}{\mathrm{3}}\:=\:\frac{\mathrm{18}}{\mathrm{3}} \\ $$$$\boldsymbol{{x}}\:=\:\mathrm{6} \\ $$$$\boldsymbol{{am}}\:\boldsymbol{{i}}\:\boldsymbol{{correct}}? \\ $$

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