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Question Number 137925 Answers: 0 Comments: 0

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Calculate ∫_(−(π/6)) ^0 ((cos^2 x)/(1−2sinx))dx

$${Calculate} \\ $$$$\underset{−\frac{\pi}{\mathrm{6}}} {\overset{\mathrm{0}} {\int}}\frac{{cos}^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{2}{sinx}}{dx} \\ $$

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Given the series a_n = 3a_(n−1) + 2a_(n−2) with a_1 =11 & a_2 = 21. Find a_n .

$${Given}\:{the}\:{series}\: \\ $$$${a}_{{n}} =\:\mathrm{3}{a}_{{n}−\mathrm{1}} +\:\mathrm{2}{a}_{{n}−\mathrm{2}} \:{with}\: \\ $$$${a}_{\mathrm{1}} =\mathrm{11}\:\&\:{a}_{\mathrm{2}} \:=\:\mathrm{21}.\:{Find}\:{a}_{{n}} . \\ $$

Question Number 137896 Answers: 0 Comments: 0

∫^( ∞) _0 ((x^3 +x+1)/( (x)^(1/3) (x^4 +x^2 +1))) dx =?

$$\underset{\mathrm{0}} {\int}^{\:\infty} \:\frac{{x}^{\mathrm{3}} +{x}+\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{x}}\:\left({x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}\right)}\:{dx}\:=? \\ $$

Question Number 137894 Answers: 2 Comments: 0

∫_0 ^(π/2) ln^2 (sinx)dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}^{\mathrm{2}} \left(\mathrm{sinx}\right)\mathrm{dx} \\ $$

Question Number 137893 Answers: 2 Comments: 0

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∫_1 ^5 ((1+(((x−1)(x−3)(x−5)))^(1/5) cos πx)/(x^2 −6x+10)) dx

$$\underset{\mathrm{1}} {\overset{\mathrm{5}} {\int}}\:\frac{\mathrm{1}+\sqrt[{\mathrm{5}}]{\left({x}−\mathrm{1}\right)\left({x}−\mathrm{3}\right)\left({x}−\mathrm{5}\right)}\:\mathrm{cos}\:\pi{x}}{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{10}}\:{dx}\: \\ $$

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Proof by mathematical induction that f(n) = n^3 + 5n is a multiple of 6.

$$\mathrm{Proof}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{that}\: \\ $$$$\:{f}\left({n}\right)\:=\:{n}^{\mathrm{3}} \:+\:\mathrm{5}{n}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{6}. \\ $$

Question Number 137874 Answers: 1 Comments: 0

.......nice ... .... calculus.... evaluate :: Ω=∫_0 ^( 1) (((ln(1−x))/x))^3 =?....

$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:.......{nice}\:...\:....\:{calculus}.... \\ $$$$\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{ln}\left(\mathrm{1}−{x}\right)}{{x}}\right)^{\mathrm{3}} =?.... \\ $$

Question Number 137871 Answers: 0 Comments: 0

Find the area bounded by the standard normal distribution p(−1.96≤Z≤2.5)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{standard} \\ $$$$\mathrm{normal}\:\mathrm{distribution}\:\mathrm{p}\left(−\mathrm{1}.\mathrm{96}\leqslant\mathrm{Z}\leqslant\mathrm{2}.\mathrm{5}\right) \\ $$

Question Number 137869 Answers: 0 Comments: 0

prove that Arg(z) is harmonic function and find the conjecate this ?

$${prove}\:{that}\:{Arg}\left({z}\right)\:{is}\:{harmonic}\:{function} \\ $$$${and}\:{find}\:{the}\:{conjecate}\:{this}\:? \\ $$

Question Number 137864 Answers: 0 Comments: 4

if , acosα+bcosβ=Acos∅ proof that asinα+bsinβ=Asin∅

$$\:\mathrm{if}\:, \\ $$$$\:\:\:\:\mathrm{acos}\alpha+\mathrm{bcos}\beta=\mathrm{Acos}\emptyset \\ $$$$\:\mathrm{proof}\:\mathrm{that}\: \\ $$$$\:\:\:\:\mathrm{asin}\alpha+\mathrm{bsin}\beta=\mathrm{Asin}\emptyset \\ $$

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If 2^(2sin^2 θ−3sin θ+1) + 2^(2−2sin^2 θ+3sin θ) = 9 find the value of sin θ+cos θ .

$${If}\:\mathrm{2}^{\mathrm{2sin}\:^{\mathrm{2}} \theta−\mathrm{3sin}\:\theta+\mathrm{1}} \:+\:\mathrm{2}^{\mathrm{2}−\mathrm{2sin}\:^{\mathrm{2}} \theta+\mathrm{3sin}\:\theta} \:=\:\mathrm{9} \\ $$$${find}\:{the}\:{value}\:{of}\:\mathrm{sin}\:\theta+\mathrm{cos}\:\theta\:. \\ $$

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