Question and Answers Forum

let give ϕ(x) =x ,ϕ 2π periodique even developp f at fourier series then find the value of Σ_(n=1) ^∞ (((−1)^n )/n^2 ) and Σ_(n=0) ^∞ (1/((2n+1)^2 )) .

$l e t g i v e φ (x) = x, φ 2 π p e r i o d i q u e e v e n$ $d e v e l o p p f a t f o u r i e r s e r i e s t h e n f i n d t h e v a l u e o f$ $\sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{n^{2}} a n d \sum_{n = 0}^{\infty} \frac{1}{{(2 n + 1)}^{2}} .$

Question Number 28832 Answers: 0 Comments: 0

find the value of A_n = ∫_1 ^(+∞) (dt/(t^(n+1) (√(t−1)))) .withn∈N .

$f i n d t h e v a l u e o f A_{n} = \int_{1}^{+ \infty} \frac{d t}{t^{n + 1} \sqrt{t - 1}} . w i t h n \in N .$

Question Number 28830 Answers: 0 Comments: 0

let give f(x)= ch(αx) and 2π periodic with α≠0 developp f at fourier series.

$l e t g i v e f (x) = c h (α x) a n d 2 π p e r i o d i c w i t h α \neq 0$ $d e v e l o p p f a t f o u r i e r s e r i e s .$

Question Number 28828 Answers: 0 Comments: 0

find f(x)=∫_0 ^1 ln(1+xt^2 )dt with ∣x∣<1 .

$f i n d f (x) = \int_{0}^{1} l n (1 + {x t}^{2}) d t w i t h ∣ x ∣< 1 .$

Question Number 28827 Answers: 0 Comments: 0

let give F(x)=∫_0 ^∞ ((arctan(1+x(1+t^2 )))/(1+t^2 ))dt and x>0 calculate (dF/dx)(x).

$l e t g i v e F (x) = \int_{0}^{\infty} \frac{a r c t a n (1 + x (1 + t^{2}))}{1 + t^{2}} d t a n d x > 0$ $c a l c u l a t e \frac{d F}{d x} (x) .$

Question Number 28826 Answers: 0 Comments: 0

let give f(x)= e^(−x) cosx and 2π periodic 1) developp f at fourier series 2) find the value of Σ_(n=−∞) ^(n=+∞) (((−1)^n )/(1+n^2 )) .

$l e t g i v e f (x) = e^{- x} c o s x a n d 2 π p e r i o d i c$ $1) d e v e l o p p f a t f o u r i e r s e r i e s$ $2) f i n d t h e v a l u e o f \sum_{n = - \infty}^{n = + \infty} \frac{{(- 1)}^{n}}{1 + n^{2}} .$

Question Number 28824 Answers: 0 Comments: 0

by using residus theorem find the value of A_n = ∫_0 ^∞ (dx/(1+x^n )) with n integr and n≥2.

$b y u s i n g r e s i d u s t h e o r e m f i n d t h e v a l u e o f$ $A_{n} = \int_{0}^{\infty} \frac{d x}{1 + x^{n}} w i t h n i n t e g r a n d n ⩾ 2 .$

Question Number 28823 Answers: 0 Comments: 0

find I = ∫_(−∞) ^(+∞) (((x−1)cosx)/(x^2 −2x+2))dx and J= ∫_(−∞) ^(+∞) (((x−1)sinx)/(x^2 −2x +2)) dx.

$f i n d I = \int_{- \infty}^{+ \infty} \frac{(x - 1) c o s x}{x^{2} - 2 x + 2} d x a n d$ $J = \int_{- \infty}^{+ \infty} \frac{(x - 1) s i n x}{x^{2} - 2 x + 2} d x .$

Question Number 28820 Answers: 0 Comments: 0

find the value of ∫_0 ^1 ((ln(1−(t^2 /4)))/t^2 )dt.

$f i n d t h e v a l u e o f \int_{0}^{1} \frac{l n (1 - \frac{t^{2}}{4})}{t^{2}} d t .$

Question Number 28819 Answers: 0 Comments: 0

let give f(x)= ∫_0 ^1 ((ln(1−x^2 t^2 ))/t^2 )dt with ∣x∣<1 by using derivation under ∫ find the value of f(x).

$l e t g i v e f (x) = \int_{0}^{1} \frac{l n (1 - x^{2} t^{2})}{t^{2}} d t w i t h ∣ x ∣< 1$ $b y u s i n g d e r i v a t i o n u n d e r \int f i n d t h e v a l u e o f f (x) .$

Question Number 28817 Answers: 0 Comments: 0

let give f(x)=e^(iαx) 2π prriodic and α ∈R−Z developp f at fourier series.

$l e t g i v e f (x) = e^{i α x} 2 π p r r i o d i c a n d α \in R - Z$ $d e v e l o p p f a t f o u r i e r s e r i e s .$

Question Number 28816 Answers: 0 Comments: 0

find the value of I= ∫_0 ^π (dθ/(1+cos^4 θ)) .

$f i n d t h e v a l u e o f I = \int_{0}^{π} \frac{d θ}{1 + {c o s}^{4} θ} .$

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