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AllQuestion and Answers: Page 511

Question Number 162924 Answers: 2 Comments: 0

𝛗 =∫_0 ^( ∞) (( e^( −x^( 2) ) .ln( x ))/( (√x))) dx=λ Γ((1/4)) λ=? ■

$ϕ = \int_{0}^{\infty} \frac{e^{- x^{2}} . \ln (x)}{\sqrt{x}} d x = λ Γ (\frac{1}{4})$ $λ = ? ◼$

Question Number 162894 Answers: 1 Comments: 0

Question Number 162893 Answers: 2 Comments: 0

Ω=∫_0 ^( 1) ((( x^ )/(ln^ ( 1−x ))))^( 2) dx=^? ln ((( 27)/(16)) ) −−−−

$Ω = \int_{0}^{1} {(\frac{x^{}}{\ln^{} (1 - x)})}^{2} d x \overset{?}{=} \ln (\frac{27}{16})$ $- - - -$

Question Number 162877 Answers: 2 Comments: 0

Find: 𝛀 = ∫_( 0) ^( 1) (x^3 /(ln^2 (1 - x))) dx

$Find :$ $Ω = \underset{0}{\int^{1}} \frac{x^{3}}{\ln^{2} (1 - x)} dx$

Question Number 162876 Answers: 0 Comments: 0

Prove that: ∫_( 0) ^( (𝛑/2)) (xcotx ∙ lncos^2 x + ln^2 cosx)dx = (π^3 /(24))

$Prove that :$ $\underset{0}{\int^{\frac{π}{2}}} (xcot x \cdot {lncos}^{2} x + \ln^{2} \cos x) dx = \frac{π^{3}}{24}$

Question Number 162872 Answers: 1 Comments: 1

Question Number 162866 Answers: 1 Comments: 0

Question Number 162865 Answers: 0 Comments: 4

Question Number 162864 Answers: 2 Comments: 0

Question Number 162860 Answers: 2 Comments: 0

Question Number 162859 Answers: 0 Comments: 0

Prove that: ∫_( 0) ^( (𝛑/2)) ((e^(cos 2x) ∙ sin(x + sin 2x))/(sin x)) dx = ((πe)/2)

$Prove that :$ $\underset{0}{\int^{\frac{π}{2}}} \frac{e^{\cos 2 x} \cdot \sin (x + \sin 2 x)}{\sin x} dx = \frac{π e}{2}$

Question Number 162856 Answers: 0 Comments: 0

Question Number 162854 Answers: 0 Comments: 0

let a;b;c≥0 and a+b+c=3 prove that: ((a - 1)/( (√(b + 3)))) + ((b - 1)/( (√(c + 3)))) + ((c - 1)/( (√(a + 3)))) ≥ 0

$let a; b; c ⩾ 0 and a + b + c = 3 prove that :$ $\frac{a - 1}{\sqrt{b + 3}} + \frac{b - 1}{\sqrt{c + 3}} + \frac{c - 1}{\sqrt{a + 3}} ⩾ 0$

Question Number 162847 Answers: 2 Comments: 0

Question Number 162845 Answers: 1 Comments: 1

Question Number 162834 Answers: 5 Comments: 0

Question Number 162833 Answers: 1 Comments: 0

Question Number 162827 Answers: 1 Comments: 0

Question Number 162825 Answers: 2 Comments: 0

Question Number 162823 Answers: 2 Comments: 0

Given: x.p(x−1)=(x−5).p(x) and p(−1)=1. Find p((1/2)).

$G i v e n : x . p (x - 1) = (x - 5) . p (x)$ $a n d p (- 1) = 1 .$ $F i n d p (\frac{1}{2}) .$

Question Number 163727 Answers: 0 Comments: 0

Question Number 163724 Answers: 0 Comments: 0

Question Number 162819 Answers: 0 Comments: 1

#combinatorial mathematics# In how many subsets of 10 members of the set , { 1, 2, ..., 20 } is there no difference between two members of 5 ? a: 2^( 10) b : 3^( 5) c : 2^( 8) d: 10^( 4)

$You can't use 'macro parameter character #' in math mode$ $I n h o w m a n y s u b s e t s o f 10$ $m e m b e r s o f t h e s e t, {1, 2, . . ., 20}$ $i s t h e r e n o d i f f e r e n c e b e t w e e n$ $t w o m e m b e r s o f 5 ?$ $a : 2^{10} b : 3^{5} c : 2^{8} d : 10^{4}$

Question Number 162814 Answers: 2 Comments: 0

Question Number 162811 Answers: 1 Comments: 0

I = ∫_0 ^( ∞) (( tan^( −1) (x ))/(( 1+x^( 2) )^( 2) )) dx = ? −−−−−−−−−−

$I = \int_{0}^{\infty} \frac{{t a n}^{- 1} (x)}{{(1 + x^{2})}^{2}} d x = ?$ $- - - - - - - - - -$

Question Number 162809 Answers: 2 Comments: 0

if y = x + (1/(x+(1/(x+(1/x)._._._._. )))) find y^′

$i f y = x + \frac{1}{x + \frac{1}{x + \frac{1}{x} ._{._{._{._{.}}}}}} f i n d y^{^{'}}$

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