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Question Number 206674 Answers: 1 Comments: 0

Question Number 206659 Answers: 2 Comments: 0

Question Number 206791 Answers: 0 Comments: 3

∫_0 ^1 (√(1−(√x))).ln^2 x dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−\sqrt{\mathrm{x}}}.\mathrm{ln}^{\mathrm{2}} \mathrm{x}\:\mathrm{dx} \\ $$

Question Number 206645 Answers: 1 Comments: 5

Let f(x)=x(x−10) and let A be the region enclosed within the following points (2,7),(8,7),(2,4),(8,4) what is the average arc length of a∙f(x) inside A,a∈R^−

$$\mathrm{Let}\:{f}\left({x}\right)={x}\left({x}−\mathrm{10}\right) \\ $$$$\mathrm{and}\:\mathrm{let}\:\mathrm{A}\:\mathrm{be}\:\mathrm{the}\:\mathrm{region}\:\mathrm{enclosed}\:\mathrm{within} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{points} \\ $$$$\left(\mathrm{2},\mathrm{7}\right),\left(\mathrm{8},\mathrm{7}\right),\left(\mathrm{2},\mathrm{4}\right),\left(\mathrm{8},\mathrm{4}\right) \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{average}\:\mathrm{arc}\:\mathrm{length}\:\mathrm{of}\:\mathrm{a}\centerdot{f}\left({x}\right) \\ $$$$\mathrm{inside}\:\mathrm{A},{a}\in\mathbb{R}^{−} \\ $$

Question Number 206643 Answers: 2 Comments: 0

Question Number 206642 Answers: 0 Comments: 0

Question Number 206640 Answers: 2 Comments: 0

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Question Number 206636 Answers: 0 Comments: 1

resoudre dans N^2 l equation 2x^2 +3y^2 =35

$${resoudre}\:{dans}\:{N}^{\mathrm{2}} \:\:{l}\:{equation} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} =\mathrm{35} \\ $$

Question Number 206629 Answers: 1 Comments: 0

Question Number 206622 Answers: 2 Comments: 0

Σ_(n=2) ^4 (((2n)/3) −1) = ?

$$\sum_{{n}=\mathrm{2}} ^{\mathrm{4}} \left(\frac{\mathrm{2}{n}}{\mathrm{3}}\:−\mathrm{1}\right)\:=\:? \\ $$

Question Number 206618 Answers: 2 Comments: 0

If A = sin^4 θ + cos^4 θ then select the correct option: i) 0 < A < (1/2) ii) 1 < A < (3/2) iii) (1/2) ≤ A ≤ 1 iv) (3/2) ≤ A ≤ 2

$$\mathrm{If}\:\mathrm{A}\:=\:\mathrm{sin}^{\mathrm{4}} \theta\:+\:\mathrm{cos}^{\mathrm{4}} \theta\:\mathrm{then}\:\mathrm{select}\:\mathrm{the}\: \\ $$$$\mathrm{correct}\:\mathrm{option}: \\ $$$$\left.\mathrm{i}\right)\:\mathrm{0}\:<\:\mathrm{A}\:<\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.\mathrm{ii}\right)\:\mathrm{1}\:<\:\mathrm{A}\:<\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\left.\mathrm{iii}\right)\:\frac{\mathrm{1}}{\mathrm{2}}\:\leq\:\mathrm{A}\:\leq\:\mathrm{1} \\ $$$$\left.\mathrm{iv}\right)\:\frac{\mathrm{3}}{\mathrm{2}}\:\leq\:\mathrm{A}\:\leq\:\mathrm{2} \\ $$

Question Number 206616 Answers: 1 Comments: 0

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Question Number 206613 Answers: 2 Comments: 0

If f(x) = { ((x^2 , x ≤ 2)),((f(x−3) , x > 2)) :} Find ∫_(−1) ^( 53) f(x) dx = ?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\begin{cases}{\mathrm{x}^{\mathrm{2}} \:\:\:,\:\:\:\mathrm{x}\:\leqslant\:\mathrm{2}}\\{\mathrm{f}\left(\mathrm{x}−\mathrm{3}\right)\:\:\:,\:\:\:\mathrm{x}\:>\:\mathrm{2}}\end{cases} \\ $$$$\mathrm{Find}\:\:\:\int_{−\mathrm{1}} ^{\:\mathrm{53}} \:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$

Question Number 206609 Answers: 0 Comments: 0

let matrix A_(n×n) and B_(n×n) satisfying A^2 = A & B^2 = B then prove ρ(A−B) = ρ(A−AB)+ ρ(B−AB) here ρ = rank

$$\:\:\:\mathrm{let}\:\mathrm{matrix}\:\:\mathrm{A}_{\mathrm{n}×\mathrm{n}} \:\mathrm{and}\:\mathrm{B}_{\mathrm{n}×\mathrm{n}} \:\mathrm{satisfying} \\ $$$$\:\:\:\mathrm{A}^{\mathrm{2}} =\:\mathrm{A}\:\:\&\:\:\mathrm{B}^{\mathrm{2}} =\:\mathrm{B}\:\:\mathrm{then}\:\mathrm{prove} \\ $$$$\:\:\:\rho\left(\mathrm{A}−\mathrm{B}\right)\:=\:\rho\left(\mathrm{A}−\mathrm{AB}\right)+\:\:\rho\left(\mathrm{B}−\mathrm{AB}\right) \\ $$$$\:\:\:\mathrm{here}\:\rho\:=\:\mathrm{rank} \\ $$

Question Number 206608 Answers: 1 Comments: 0

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Question Number 206591 Answers: 0 Comments: 5

I have a background in building design but I have great interest in Mathematics. That′s one major reason why I joined this platform cause I did little or no maths in my undergraduate days as a building design student. This forum has contributed greatly to my current mathematical skill and I′m grateful. What textbooks and youtube channel or playlist would you recommend that I in understanding from the fundamentals to the advanced level of differential equations?

$${I}\:{have}\:{a}\:{background}\:{in}\:{building}\:{design} \\ $$$${but}\:{I}\:{have}\:{great}\:{interest}\:{in}\:{Mathematics}. \\ $$$${That}'{s}\:{one}\:{major}\:{reason}\:{why}\:{I}\:{joined} \\ $$$${this}\:{platform}\:{cause}\:{I}\:{did}\:{little}\:{or}\:{no} \\ $$$${maths}\:{in}\:{my}\:{undergraduate}\:{days}\:{as}\:{a} \\ $$$${building}\:{design}\:{student}. \\ $$$$ \\ $$$${This}\:{forum}\:{has}\:{contributed}\:{greatly}\:{to} \\ $$$${my}\:{current}\:{mathematical}\:{skill}\:{and} \\ $$$${I}'{m}\:{grateful}. \\ $$$$ \\ $$$$ \\ $$$${What}\:{textbooks}\:{and}\:{youtube}\:{channel}\:{or} \\ $$$${playlist}\:{would}\:{you}\:{recommend}\:{that}\:{I} \\ $$$${in}\:{understanding}\:{from}\:\:{the}\:{fundamentals} \\ $$$${to}\:{the}\:{advanced}\:{level}\:{of}\:{differential} \\ $$$${equations}? \\ $$$$ \\ $$

Question Number 206579 Answers: 1 Comments: 0

Evaluate : ∫_0 ^1 ((ln (1+x^2 ))/(1+x))d(x).

$$\mathrm{Evaluate}\::\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}}{d}\left({x}\right). \\ $$

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