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IntegrationQuestion and Answers: Page 82

Question Number 141437 Answers: 0 Comments: 0

Question Number 141419 Answers: 2 Comments: 0

𝛗:=∫_0 ^( ∞) ((ln(cosh(x)))/(cosh(x)))dx=^? ∫_0 ^( (π/2)) log((1/(sin(x))))dx

$ϕ := \int_{0}^{\infty} \frac{l n (c o s h (x))}{c o s h (x)} d x \overset{?}{=} \int_{0}^{\frac{π}{2}} l o g (\frac{1}{s i n (x)}) d x$

Question Number 141407 Answers: 2 Comments: 0

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

$Ω := \int_{0}^{\infty} \frac{d x}{{(x^{4} - x^{2} + 1)}^{3}} = ?$

Question Number 141360 Answers: 0 Comments: 1

∫_0 ^(π/2) (√(cosxsenx))dx

$\int_{0}^{π / 2} \sqrt{c o s x s e n x} d x$

Question Number 141362 Answers: 1 Comments: 0

∫sen(2θ)cos^4 (2θ)dθ

$\int s e n (2 θ) {c o s}^{4} (2 θ) d θ$

Question Number 141336 Answers: 2 Comments: 0

∫sin (ln (x))dx=? Please

$\int \sin (\ln (x)) d x = ? P l e a s e$

Question Number 141417 Answers: 2 Comments: 0

........ advanced ... ... ... calculus....... prove that:: F:= ∫_(−1) ^( 0) ((e^x +e^(1/x) −1)/x) dx=^(??) γ

$. . . . . . . . a d v a n c e d . . . . . . . . . c a l c u l u s . . . . . . .$ $p r o v e t h a t ::$ $F := \int_{- 1}^{0} \frac{e^{x} + e^{\frac{1}{x}} - 1}{x} d x \overset{? ?}{=} γ$

Question Number 141333 Answers: 1 Comments: 0

∫x^2 cos ((x/2))dx

$\int x^{2} \cos (\frac{x}{2}) d x$

Question Number 141319 Answers: 2 Comments: 0

prove:: Ω:=∫_0 ^( 1) ((ln^2 (x))/(1−x^4 ))dx =(π^3 /(32))+(7/8)ζ(3)..

$p r o v e ::$ $Ω := \int_{0}^{1} \frac{{l n}^{2} (x)}{1 - x^{4}} d x = \frac{π^{3}}{32} + \frac{7}{8} ζ (3) . .$

Question Number 141373 Answers: 1 Comments: 1

Question Number 141367 Answers: 1 Comments: 0

∫((√(cosx∙senx)))dx

$\int (\sqrt{c o s x \cdot s e n x}) d x$

Question Number 141388 Answers: 1 Comments: 0

∫_0 ^(π/2) (√((senx∙cosx)))dx Help

$\int_{0}^{π / 2} \sqrt{(s e n x \cdot c o s x)} d x$ $H e l p$

Question Number 141387 Answers: 1 Comments: 0

∫_(−π/4) ^(π/4) (sec^2 x+tgx)^2 dx

$\int_{- π / 4}^{π / 4} {({s e c}^{2} x + t g x)}^{2} d x$

Question Number 141312 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (−1)^n ((Si(2πn)−(π/2))/n)=?

$\underset{n = 1}{\sum^{\infty}} {(- 1)}^{n} \frac{S i (2 π n) - \frac{π}{2}}{n} = ?$

Question Number 141249 Answers: 2 Comments: 1

Question Number 141244 Answers: 1 Comments: 1

I=∫_0 ^( ∞) ((x{(a^2 −b^2 )x−2a^2 x^2 −2b^2 }dx)/((a^2 x^2 +b^2 )^2 {(a^2 −b^2 )x+a^2 x^2 +b^2 }))

$I = \int_{0}^{\infty} \frac{x {(a^{2} - b^{2}) x - 2 a^{2} x^{2} - 2 b^{2}} d x}{{(a^{2} x^{2} + b^{2})}^{2} {(a^{2} - b^{2}) x + a^{2} x^{2} + b^{2}}}$

Question Number 141240 Answers: 0 Comments: 0

Solve using fourier′s series −y′′+y=e^(−2∣x∣)

$Solve using {fourier}^{'} s series$ $- y^{″} + y = e^{- 2 ∣ x ∣}$

Question Number 141222 Answers: 1 Comments: 0

calculate ∫_0 ^(4π) (dθ/((x^2 +2x cosθ +1)^2 ))

$calculate \int_{0}^{4 π} \frac{d θ}{{(x^{2} + 2 x \cos θ + 1)}^{2}}$

Question Number 141191 Answers: 1 Comments: 0

find the volume of the solid generated when the region bounded by the y=x y=x+2, x=2 and x=4 revolved about the x-axis

$f i n d t h e v o l u m e o f t h e s o l i d g e n e r a t e d$ $w h e n t h e r e g i o n b o u n d e d b y t h e y = x$ $y = x + 2, x = 2 a n d x = 4 r e v o l v e d a b o u t t h e x - a x i s$

Question Number 141189 Answers: 0 Comments: 3

find the area of the shaded region shown below which is boinded by to functions f(x)=x^2 g(x)=2−x and the x-axis

$f i n d t h e a r e a o f t h e s h a d e d r e g i o n$ $s h o w n b e l o w w h i c h i s b o i n d e d b y t o f u n c t i o n s$ $f (x) = x^{2} g (x) = 2 - x a n d t h e x - a x i s$

Question Number 141142 Answers: 0 Comments: 0

Question Number 141134 Answers: 1 Comments: 0

prove that:: Φ:=Σ_(m,n=1) ^∞ (((−1)^(n−1) )/(m^2 +n^2 ))= (π^2 /(24))+((πln(2))/8)

$p r o v e t h a t ::$ $Φ := \underset{m, n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n - 1}}{m^{2} + n^{2}} = \frac{π^{2}}{24} + \frac{π l n (2)}{8}$

Question Number 141133 Answers: 1 Comments: 0

I:=∫_0 ^( ∞) (((x^n −1)(x−1))/(x^(n+3) −1))dx=??

$I := \int_{0}^{\infty} \frac{(x^{n} - 1) (x - 1)}{x^{n + 3} - 1} d x = ? ?$

Question Number 141085 Answers: 2 Comments: 0

Question Number 141082 Answers: 3 Comments: 0

........ nice ....... calculus ........ 𝛗:=Σ_(n=2) ^∞ ((ζ ( n ))/(n . 4^n ))=?

$. . . . . . . . n i c e . . . . . . . c a l c u l u s . . . . . . . .$ $ϕ := \underset{n = 2}{\sum^{\infty}} \frac{ζ (n)}{n . 4^{n}} = ?$

Question Number 141031 Answers: 0 Comments: 0

∫_(π/6) ^( π/3) (√(1+((cos^2 x)/(sin x)))) dx ?

$\int_{π / 6}^{π / 3} \sqrt{1 + \frac{\cos^{2} x}{\sin x}} d x ?$

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