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IntegrationQuestion and Answers: Page 285

Question Number 36393 Answers: 0 Comments: 0

let f(x) = (2/(sinx)) ,2π periodic odd developp f at fourier serie .

$l e t f (x) = \frac{2}{s i n x}, 2 π p e r i o d i c o d d$ $d e v e l o p p f a t f o u r i e r s e r i e .$

Question Number 36336 Answers: 0 Comments: 4

find f(x)= ∫_0 ^∞ arctan(xt^2 )dt with x>0

$f i n d f (x) = \int_{0}^{\infty} a r c t a n ({x t}^{2}) d t w i t h x > 0$

Question Number 36335 Answers: 0 Comments: 1

find f(t) = ∫_0 ^1 arctan(tx^2 )dx with t≥0 developp f at integr serie

$f i n d f (t) = \int_{0}^{1} a r c t a n ({t x}^{2}) d x w i t h t ⩾ 0$ $d e v e l o p p f a t i n t e g r s e r i e$

Question Number 36205 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((x^2 −1)/((x^2 +1)^2 )) x^(1/3) dx

$c a l c u l a t e \int_{0}^{\infty} \frac{x^{2} - 1}{{(x^{2} + 1)}^{2}} x^{\frac{1}{3}} d x$

Question Number 36204 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ ((x^2 −1)/(x^2 +1)) ((sin(x))/x)dx

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

Question Number 36203 Answers: 0 Comments: 1

let f(t) = ∫_0 ^∞ ((cos(tx))/((2+x^2 )^2 ))dx 1) find a simple form of f(t) 2) calculate ∫_0 ^∞ ((cos(3x))/((2+x^2 )^2 ))dx

$l e t f (t) = \int_{0}^{\infty} \frac{c o s (t x)}{{(2 + x^{2})}^{2}} d x$ $1) f i n d a s i m p l e f o r m o f f (t)$ $2) c a l c u l a t e \int_{0}^{\infty} \frac{c o s (3 x)}{{(2 + x^{2})}^{2}} d x$

Question Number 36202 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((x^2 dx)/((x^2 +1)^3 ))

$c a l c u l a t e \int_{0}^{\infty} \frac{x^{2} d x}{{(x^{2} + 1)}^{3}}$

Question Number 36201 Answers: 0 Comments: 1

calculate ∫_0 ^(π/2) (dθ/(1+2sin^2 θ))

$c a l c u l a t e \int_{0}^{\frac{π}{2}} \frac{d θ}{1 + 2 {s i n}^{2} θ}$

Question Number 36200 Answers: 0 Comments: 4

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

$c a l c u l a t e \int_{0}^{2 π} \frac{d θ}{{(2 + c o s θ)}^{2}}$

Question Number 36198 Answers: 0 Comments: 1

let f(z) = ((z^2 +1)/(z^4 −1)) find (a_(k)) the poles of f and calculate Res(f,a_k )

$l e t f (z) = \frac{z^{2} + 1}{z^{4} - 1}$ $f i n d (a_{k)} t h e p o l e s o f f a n d c a l c u l a t e$ $R e s (f, a_{k})$

Question Number 36197 Answers: 0 Comments: 1

find the value of ∫_0 ^(2π) (dx/(cos^2 x +3 sin^2 x))

$f i n d t h e v a l u e o f \int_{0}^{2 π} \frac{d x}{{c o s}^{2} x + 3 {s i n}^{2} x}$

Question Number 36196 Answers: 0 Comments: 0

let ρ>0 and C the circle x^2 +y^2 =ρ^2 calculate ∫_C ydx +xy dy

$l e t ρ > 0 a n d C t h e c i r c l e x^{2} + y^{2} = ρ^{2}$ $c a l c u l a t e \int_{C} y d x + x y d y$

Question Number 36195 Answers: 0 Comments: 1

let C ={(x,y)∈R^2 / 0≤x≤1 and y=2x^2 } calculate ∫_C x^2 ydx +(x^2 −y^2 )dy

$l e t C = {(x, y) \in R^{2} / 0 ⩽ x ⩽ 1 a n d y = 2 x^{2}}$ $c a l c u l a t e \int_{C} x^{2} y d x + (x^{2} - y^{2}) d y$

Question Number 36194 Answers: 0 Comments: 0

let D ={(x,y,z)∈R^2 / 0<z<1 and x^2 +y^2 <z^2 } calculate ∫∫_D xyzdxdydz

$l e t D = {(x, y, z) \in R^{2} / 0 < z < 1 a n d x^{2} + y^{2} < z^{2}}$ $c a l c u l a t e \int \int_{D} x y z d x d y d z$

Question Number 36193 Answers: 0 Comments: 1

let D ={(x,y)∈ R^2 / x^2 +y^2 −x<0 and x^2 +y^2 −y >0 and y>0} calculate∫∫_D (x+y)^2 dxdy

$l e t D = {(x, y) \in R^{2} / x^{2} + y^{2} - x < 0 a n d$ $x^{2} + y^{2} - y > 0 a n d y > 0}$ $c a l c u l a t e \int \int_{D} {(x + y)}^{2} d x d y$

Question Number 36192 Answers: 0 Comments: 1

let D ={(x,y)∈ R^2 /x^2 +y^2 <1} find the value of ∫∫_D ((dxdy)/(x^2 +y^(2 ) + 2))

$l e t D = {(x, y) \in R^{2} / x^{2} + y^{2} < 1}$ $f i n d t h e v a l u e o f \int \int_{D} \frac{d x d y}{x^{2} + y^{2} + 2}$

Question Number 36190 Answers: 0 Comments: 1

calculate ∫∫_D (x+y)e^(x+y) dxdy with D = {(x,y)∈R^2 / 0<x<2 and 1<y<2 }

$c a l c u l a t e \int \int_{D} (x + y) e^{x + y} d x d y w i t h$ $D = {(x, y) \in R^{2} / 0 < x < 2 a n d 1 < y < 2}$

Question Number 36189 Answers: 0 Comments: 1

let F(x)=∫_0 ^∞ ((e^(−x^2 t) (√t))/(1+t^2 ))dt calculate lim_(x→+∞) F(x) .

$l e t F (x) = \int_{0}^{\infty} \frac{e^{- x^{2} t} \sqrt{t}}{1 + t^{2}} d t$ $c a l c u l a t e {l i m}_{x \to + \infty} F (x) .$

Question Number 36188 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ ((√t)/(1+t^2 ))dt

$f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{\sqrt{t}}{1 + t^{2}} d t$

Question Number 36187 Answers: 0 Comments: 3

let I_n (x)= ∫_0 ^∞ ((t sin(t))/((t^2 +x^2 )^n ))dt 1) find a relation between I_(n+1) and I_n 2) calculate I_2 (x) and I_3 (x) 3) calculate ∫_0 ^∞ ((tsin(t))/((2+t^2 )^2 ))dt

$l e t I_{n} (x) = \int_{0}^{\infty} \frac{t s i n (t)}{{(t^{2} + x^{2})}^{n}} d t$ $1) f i n d a r e l a t i o n b e t w e e n I_{n + 1} a n d I_{n}$ $2) c a l c u l a t e I_{2} (x) a n d I_{3} (x)$ $3) c a l c u l a t e \int_{0}^{\infty} \frac{t s i n (t)}{{(2 + t^{2})}^{2}} d t$

Question Number 36186 Answers: 0 Comments: 1

find nature of ∫_1 ^(+∞) (√t) sin(t^2 )dt .

$f i n d n a t u r e o f \int_{1}^{+ \infty} \sqrt{t} s i n (t^{2}) d t .$

Question Number 36185 Answers: 0 Comments: 2

study the vonvergence of ∫_1 ^(+∞) ((e^(−(1/t)) −cos((1/t)))/t)dt

$s t u d y t h e v o n v e r g e n c e o f$ $\int_{1}^{+ \infty} \frac{e^{- \frac{1}{t}} - c o s (\frac{1}{t})}{t} d t$

Question Number 36184 Answers: 0 Comments: 1

study the convergence of ∫_1 ^(+∞) ((cos(t))/(√t))dt

$s t u d y t h e c o n v e r g e n c e o f \int_{1}^{+ \infty} \frac{c o s (t)}{\sqrt{t}} d t$

Question Number 36183 Answers: 0 Comments: 0

calculate ∫_1 ^(+∞) arctan((1/t))dt

$c a l c u l a t e \int_{1}^{+ \infty} a r c t a n (\frac{1}{t}) d t$

Question Number 36182 Answers: 2 Comments: 1

calculate ∫_1 ^(+∞) (dt/(t(√(1+t^2 ))))

$c a l c u l a t e \int_{1}^{+ \infty} \frac{d t}{t \sqrt{1 + t^{2}}}$

Question Number 36181 Answers: 0 Comments: 1

let I(ξ) = ∫_ξ ^(1−ξ) (dt/(1−(t−ξ)^2 )) find lim_(ξ→0^+ ) I(ξ)

$l e t I (ξ) = \int_{ξ}^{1 - ξ} \frac{d t}{1 - {(t - ξ)}^{2}}$ $f i n d {l i m}_{ξ \to 0^{+}} I (ξ)$

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