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Question Number 65040 Answers: 0 Comments: 0

what is the curve of the curve caused by the earth to the space time _ fabric

$${what}\:{is}\:{the}\:{curve}\:{of}\:{the}\:{curve}\:{caused}\:\:{by} \\ $$$${the}\:{earth}\:{to}\:{the}\:{space}\:{time}\:\_\:{fabric} \\ $$

Question Number 65022 Answers: 1 Comments: 4

Question Number 65015 Answers: 1 Comments: 3

∫(((√(x+1)) − (√(x−1)))/((√(x+1)) + (√(x−1)))) dx

$$\int\frac{\sqrt{{x}+\mathrm{1}}\:−\:\sqrt{{x}−\mathrm{1}}}{\sqrt{{x}+\mathrm{1}}\:+\:\sqrt{{x}−\mathrm{1}}}\:{dx} \\ $$

Question Number 65013 Answers: 1 Comments: 0

why do we divide each term by n when given the question lim_(x→∞) ((3 +2n)/(1+n)) ?

$${why}\:{do}\:{we}\:{divide}\:{each}\:{term}\:{by}\:{n}\:{when}\:{given}\:{the}\:{question} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3}\:+\mathrm{2}{n}}{\mathrm{1}+{n}}\:? \\ $$

Question Number 65011 Answers: 5 Comments: 1

1.(i)Evaluate:∫(1/(sin x−cos x+(√2)))dx (ii)Evaluate:∫2^2^2^x 2^2^x 2^x dx (iii)Evaluate:∫((cos^3 x)/(sin^2 x+sin x))dx 2.cosec [tan^(−1) {cos (cot^(−1) (sec(sin^(−1) a)))}]=What? 3.Prove that, sin [cot^(−1) {cos (tan^(−1) x)}]=(√((x^2 +1)/(x^2 +2))) 4.Mention Order and Degree and state also if it is linear or non-linear. y+(d^2 y/dx^2 )=((19)/(25))∫y^2 dx

$$\mathrm{1}.\left(\mathrm{i}\right)\mathrm{Evaluate}:\int\frac{\mathrm{1}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}+\sqrt{\mathrm{2}}}{dx} \\ $$$$\left(\mathrm{ii}\right)\mathrm{Evaluate}:\int\mathrm{2}^{\mathrm{2}^{\mathrm{2}^{{x}} } } \mathrm{2}^{\mathrm{2}^{{x}} } \mathrm{2}^{{x}} \:{dx} \\ $$$$\left(\mathrm{iii}\right)\mathrm{Evaluate}:\int\frac{\mathrm{cos}\:^{\mathrm{3}} {x}}{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{sin}\:{x}}{dx} \\ $$$$\mathrm{2}.\mathrm{cosec}\:\left[\mathrm{tan}^{−\mathrm{1}} \left\{\mathrm{cos}\:\left(\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{sec}\left(\mathrm{sin}^{−\mathrm{1}} {a}\right)\right)\right)\right\}\right]=\mathrm{What}? \\ $$$$\mathrm{3}.\mathrm{Prove}\:\mathrm{that},\:\:\mathrm{sin}\:\left[\mathrm{cot}^{−\mathrm{1}} \left\{\mathrm{cos}\:\left(\mathrm{tan}^{−\mathrm{1}} {x}\right)\right\}\right]=\sqrt{\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{2}}} \\ $$$$\mathrm{4}.\mathrm{Mention}\:\mathrm{Order}\:\mathrm{and}\:\mathrm{Degree}\:\mathrm{and}\:\:\mathrm{state}\:\mathrm{also}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{linear}\:\mathrm{or}\:\mathrm{non}-{l}\mathrm{inear}. \\ $$$$\:\:\:\:\:{y}+\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\frac{\mathrm{19}}{\mathrm{25}}\int{y}^{\mathrm{2}} \:{dx} \\ $$

Question Number 65004 Answers: 0 Comments: 1

let U_n = ∫_(1/n) ^(2/n) Γ(x)Γ(1−x)dx with n≥3 1) calculate and determine lim_(n→+∞) U_n 2) study the convergence of Σ U_n

$${let}\:{U}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{\frac{\mathrm{2}}{{n}}} \:\Gamma\left({x}\right)\Gamma\left(\mathrm{1}−{x}\right){dx}\:\:\:\:{with}\:{n}\geqslant\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{and}\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 65003 Answers: 0 Comments: 0

find ∫_0 ^∞ (dx/(Γ(x))) with Γ(x) =∫_0 ^∞ t^(x−1) e^(−t) dt (x>0)

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\Gamma\left({x}\right)}\:\:{with}\:\:\Gamma\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\:\:\left({x}>\mathrm{0}\right) \\ $$

Question Number 64994 Answers: 1 Comments: 1

∫(√(tanh(x))) dx

$$\int\sqrt{{tanh}\left({x}\right)}\:{dx} \\ $$

Question Number 64993 Answers: 0 Comments: 0

let f(a) =∫_0 ^∞ ((cos(x^2 )−sin(x^2 ))/((x^2 +a^2 )^2 ))dx with a>0 1) calculate f(a) 2) find the values of ∫_0 ^∞ ((cos(x^2 )−sin(x^2 ))/((x^2 +1)^2 )) and ∫_0 ^∞ ((cos(x^2 )−sin(x^2 ))/((x^2 +3)^2 ))dx .

Question Number 64984 Answers: 1 Comments: 2

∫_0 ^3 x ∣x^2 − x − 2∣ dx = ?

$$\underset{\mathrm{0}} {\int}\:\overset{\mathrm{3}} {\:}\:{x}\:\mid{x}^{\mathrm{2}} \:−\:{x}\:−\:\mathrm{2}\mid\:{dx}\:\:=\:\:? \\ $$

Question Number 64975 Answers: 0 Comments: 1

Question Number 64973 Answers: 1 Comments: 0

Question Number 64971 Answers: 0 Comments: 3

Question Number 64970 Answers: 0 Comments: 9

let f(a)=∫_0 ^∞ ((cos(x^2 ) +sin(x^2 ))/((x^2 +a^2 )^2 )) dx with a>0 1) calculate f(a) 2) find the values of ∫_0 ^∞ ((cos(x^2 )+sin(x^2 ))/((x^2 +1)^2 ))dx and ∫_0 ^∞ ((cos(x^2 )+sin(x^2 ))/((x^2 +3)^2 ))dx

Question Number 64968 Answers: 0 Comments: 1