Question and Answers Forum

...nice calculus... calculate ::: Ω=^(???) ∫_0 ^( ∞) e^( −t) t^( 2) j_0 ( t )dt where : j_((v)) (x)=x^v Σ_(n=0) ^( ∞) (((−1)^n x^(2n) )/(2^(2n+v) n!Γ(n+v+1))) ::: Bessel function of the first type of order v ... j_v (x) is convergent (why?): ∀x∈R...

$. . . n i c e c a l c u l u s . . .$ $c a l c u l a t e :::$ $Ω \overset{? ? ?}{=} \int_{0}^{\infty} e^{- t} t^{2} j_{0} (t) d t$ $w h e r e : j_{(v)} (x) = x^{v} \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n} x^{2 n}}{2^{2 n + v} n! Γ (n + v + 1)}$ $::: B e s s e l f u n c t i o n o f$ $t h e f i r s t t y p e o f o r d e r v . . .$ $j_{v} (x) i s c o n v e r g e n t (w h y ?) : \forall x \in R . . .$

Question Number 126274 Answers: 2 Comments: 0

Question Number 126273 Answers: 1 Comments: 2

Question Number 126266 Answers: 1 Comments: 0

solve ∫_0 ^( 1) ((1−x^2 )/((1+x^2 )(√(1+x^4 )))) dx ?

$s o l v e \int_{0}^{1} \frac{1 - x^{2}}{(1 + x^{2}) \sqrt{1 + x^{4}}} d x ?$

Question Number 126230 Answers: 2 Comments: 0

∫ e^( cos^(− 1) (x)) dx

$\int e^{\cos^{- 1} (x)} dx$

Question Number 126205 Answers: 0 Comments: 0

calculate ∫∫ _([0,1]^2 ) ((dxdy)/( (√(x^2 +y^2 )) +xy))

$calculate \int \int_{{[0, 1]}^{2}} \frac{dxdy}{\sqrt{x^{2} + y^{2}} + xy}$

Question Number 126203 Answers: 3 Comments: 0

∫_0 ^∞ (1/(1+x^s +x^(2s) ))

${\int^{\infty}}_{0} \frac{1}{1 + x^{s} + x^{2 s}}$

Question Number 126183 Answers: 1 Comments: 0

∫_0 ^( ∞) ((e^(2πx) −1)/(e^(2πx) +1)) ((1/x)−(1/(N^2 +x^2 ))) dx

$\int_{0}^{\infty} \frac{e^{2 π x} - 1}{e^{2 π x} + 1} (\frac{1}{x} - \frac{1}{N^{2} + x^{2}}) d x$

Question Number 126179 Answers: 1 Comments: 0

let f(x)= e^(−2x) actan (3x+1) 1)calculste f^((n)) (x) and f^((n)) (0) 2) if f(x)=Σ a_n x^n determine the sequence a_n 3) calculate ∫_0 ^∞ f(x)dx

$let f (x) = e^{- 2 x} actan (3 x + 1)$ $1) calculste f^{(n)} (x) and f^{(n)} (0)$ $2) if f (x) = Σ a_{n} x^{n} determine the sequence a_{n}$ $3) calculate \int_{0}^{\infty} f (x) dx$

Question Number 126139 Answers: 1 Comments: 4

closed formula .... ∫_0 ^( 1) ((x^n ln(x))/(1+x))dx =?

$c l o s e d f o r m u l a . . . .$ $\int_{0}^{1} \frac{x^{n} l n (x)}{1 + x} d x = ?$

Question Number 126133 Answers: 2 Comments: 0

Question Number 126073 Answers: 0 Comments: 2

Question Number 126068 Answers: 1 Comments: 0

Question Number 126065 Answers: 1 Comments: 0

Show that:: Ω = ∫_0 ^( 1) ((Li_2 (x)log(x))/(1+x))dx = −(3/(16))ζ(4) Goodluck

$Show that ::$ $Ω = \int_{0}^{1} \frac{{Li}_{2} (x) \log (x)}{1 + x} dx = - \frac{3}{16} ζ (4)$ $Goodluck$

Question Number 126000 Answers: 3 Comments: 0

∫ (dx/((x−1)(√(x^2 −2x)))) ?

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

Question Number 125999 Answers: 2 Comments: 1

Question Number 125997 Answers: 1 Comments: 0

Find the Riemann sum for the given function with the specified number of intervals using left endpoints f(x)= 4ln x+2x ; 1≤x≤4 n=7 . Round your answer to two decimal places ?

$F i n d t h e R i e m a n n s u m f o r t h e$ $g i v e n f u n c t i o n w i t h t h e s p e c i f i e d$ $n u m b e r o f i n t e r v a l s u s i n g l e f t$ $e n d p o i n t s f (x) = 4 \ln x + 2 x; 1 ⩽ x ⩽ 4$ $n = 7 . R o u n d y o u r a n s w e r t o t w o$ $d e c i m a l p l a c e s ?$

Question Number 125986 Answers: 1 Comments: 0

Question Number 125965 Answers: 1 Comments: 0

∫ cot x ln (sin x) dx ?

$\int \cot x \ln (\sin x) d x ?$

Pg 110 Pg 111 Pg 112 Pg 113 Pg 114 Pg 115 Pg 116 Pg 117 Pg 118 Pg 119

Contact: info@tinkutara.com