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IntegrationQuestion and Answers: Page 22

Question Number 197060 Answers: 1 Comments: 1

Prove that ∫^( (π/2)) _( 0) ((ln(1+αsint))/(sint))dt= (π^2 /8)−(1/2)(arccosα)^2

$Prove that$ ${\int_{0}}^{\frac{π}{2}} \frac{\ln (1 + α \sin t)}{\sin t} d t = \frac{π^{2}}{8} - \frac{1}{2} {(\arccos α)}^{2}$

Question Number 197024 Answers: 3 Comments: 0

calculate Ω= ∫_0 ^( (π/2)) sin(x) (√( 1+^ sin(x)cos(x))) dx=?

$c a l c u l a t e$ $Ω = \int_{0}^{\frac{π}{2}} s i n (x) \sqrt{1 \overset{}{+} s i n (x) c o s (x)} d x = ?$

Question Number 196983 Answers: 3 Comments: 1

Question Number 196832 Answers: 0 Comments: 1

∫xe^(1/(2x)) dx=?

$\int x e^{\frac{1}{2 x}} d x = ?$

Question Number 196817 Answers: 1 Comments: 0

Question Number 196688 Answers: 1 Comments: 0

Question Number 196788 Answers: 2 Comments: 0

calculer ∫_0 ^1 (√(1−x^2 )) <erly rolvinst>

$c a l c u l e r \int_{0}^{1} \sqrt{1 - x^{2}}$ $< e r l y r o l v i n s t >$

Question Number 196557 Answers: 1 Comments: 0

Question Number 196496 Answers: 1 Comments: 0

Question Number 196487 Answers: 1 Comments: 0

∫(sec^4 x−cot^4 x)dx

$\int (\sec^{4} x - \cot^{4} x) d x$

Question Number 196459 Answers: 1 Comments: 0

Question Number 196436 Answers: 1 Comments: 0

∫(dx/(x(x^n −1)))

$\int \frac{d x}{x (x^{n} - 1)}$

Question Number 196435 Answers: 0 Comments: 2

Question Number 196375 Answers: 1 Comments: 1

∫(dx/(x(x^4 −1)))

$\int \frac{d x}{x (x^{4} - 1)}$

Question Number 196277 Answers: 3 Comments: 0

$\underset{―}{\underset{⏟}{}}$

Question Number 196276 Answers: 1 Comments: 0

Question Number 196173 Answers: 1 Comments: 0

Calcul I_a =∫_a ^(1/a) ((lnx)/(1+x^2 ))dx (a>0)

$C a l c u l I_{a} = \int_{a}^{\frac{1}{a}} \frac{l n x}{1 + x^{2}} d x (a > 0)$

Question Number 196046 Answers: 0 Comments: 0

∫e^x^2 ln^(24) (x)dx

$\int e^{x^{2}} {l n}^{24} (x) d x$

Question Number 196037 Answers: 2 Comments: 0

∫ ((sin 2x)/(sin^3 x+cos^3 x)) dx =?

$\int \frac{\sin 2 x}{\sin^{3} x + \cos^{3} x} dx = ?$

Question Number 196013 Answers: 1 Comments: 0

quel est la transformer de Fourier de la fonction suivante: f(x)=e^(−(x^2 /2)) Find the Fourier transform of the following fonction.

$q u e l e s t l a t r a n s f o r m e r d e F o u r i e r d e l a f o n c t i o n$ $s u i v a n t e :$ $f (x) = e^{- \frac{x^{2}}{2}}$ $F i n d t h e F o u r i e r t r a n s f o r m o f t h e$ $f o l l o w i n g f o n c t i o n .$

Question Number 195997 Answers: 0 Comments: 0

Question Number 195995 Answers: 1 Comments: 0

Δ={(x^ y z), x^2 +y^2 ≤1, x≥0,0<z<y+1} calculer I=∫∫∫_Δ xyzdxdydz please i need help

$Δ = {(\bar{x} y z), x^{2} + y^{2} ⩽ 1, x ⩾ 0, 0 < z < y + 1}$ $c a l c u l e r I = \int \int \int_{Δ} x y z d x d y d z$ $p l e a s e i n e e d h e l p$

Question Number 195910 Answers: 1 Comments: 0

Question Number 195846 Answers: 1 Comments: 0

{ (( Ω_1 = ∫_0 ^( (π/2)) (( x^( 2) )/(sin^( 2) (x))) dx )),(( ⇒ (Ω_1 /Ω_( 2) ) = ? )),(( Ω_( 2) = ∫_0 ^( (π/2)) (x/(tan(x))) dx)) :}

${\begin{cases} Ω_{1} = \int_{0}^{\frac{π}{2}} \frac{x^{2}}{{s i n}^{2} (x)} d x \\ \Rightarrow \frac{Ω_{1}}{Ω_{2}} = ? \\ Ω_{2} = \int_{0}^{\frac{π}{2}} \frac{x}{t a n (x)} d x \end{cases}$

Question Number 195803 Answers: 0 Comments: 0

∫(((√x)dx)/( (√(−1+(√(2−(x+1)^2 ))))))

$\int \frac{\sqrt{x} d x}{\sqrt{- 1 + \sqrt{2 - {(x + 1)}^{2}}}}$

Question Number 195468 Answers: 1 Comments: 0

∫((x^5 +x^2 )/((x^6 +2x^3 )^7 ))dx

$\int \frac{x^{5} + x^{2}}{{(x^{6} + 2 x^{3})}^{7}} d x$

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