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IntegrationQuestion and Answers: Page 280

Question Number 37297 Answers: 0 Comments: 1

calculate ∫_C (z/(z^2 +1))dz with C={z∈C/∣z∣=(1/2)}

$c a l c u l a t e \int_{C} \frac{z}{z^{2} + 1} d z w i t h C = {z \in C / ∣ z ∣= \frac{1}{2}}$

Question Number 37291 Answers: 0 Comments: 1

calculate g(θ) = ∫_(−∞) ^(+∞) e^(−x^2 ) sin(sinθ x^2 )dx .

$c a l c u l a t e g (θ) = \int_{- \infty}^{+ \infty} e^{- x^{2}} s i n (s i n θ x^{2}) d x .$

Question Number 37290 Answers: 0 Comments: 0

find f(θ) = ∫_(−∞) ^(+∞) e^(−x^2 ) cos(cosθx)dx .

$f i n d f (θ) = \int_{- \infty}^{+ \infty} e^{- x^{2}} c o s (c o s θ x) d x .$

Question Number 37289 Answers: 0 Comments: 0

calculate ∫_0 ^(2π) (dx/(cos^2 t +4sin^2 t))dt .

$c a l c u l a t e \int_{0}^{2 π} \frac{d x}{{c o s}^{2} t + 4 {s i n}^{2} t} d t .$

Question Number 37288 Answers: 0 Comments: 1

calculate f(α) = ∫_(−∞) ^(+∞) ((cos(2x))/(1+ax^2 )) dx with a>0 2) find the value of ∫_(−∞) ^(+∞) ((cos(2x))/(1+3x^2 )) dx .

$c a l c u l a t e f (α) = \int_{- \infty}^{+ \infty} \frac{c o s (2 x)}{1 + {a x}^{2}} d x w i t h a > 0$ $2) f i n d t h e v a l u e o f \int_{- \infty}^{+ \infty} \frac{c o s (2 x)}{1 + 3 x^{2}} d x .$

Question Number 37287 Answers: 0 Comments: 1

calculate f(t) = ∫_(−∞) ^(+∞) ((cos(tx))/(1+x^2 )) dx

$c a l c u l a t e f (t) = \int_{- \infty}^{+ \infty} \frac{c o s (t x)}{1 + x^{2}} d x$

Question Number 37285 Answers: 0 Comments: 3

let A_n = ∫_0 ^∞ e^(−nx^2 ) sin((x/n))dx with n integr not 0 1) calculate A_n 2) find lim_(n→+∞) A_n

$l e t A_{n} = \int_{0}^{\infty} e^{- {n x}^{2}} s i n (\frac{x}{n}) d x w i t h n i n t e g r n o t 0$ $1) c a l c u l a t e A_{n}$ $2) f i n d {l i m}_{n \to + \infty} A_{n}$

Question Number 37284 Answers: 0 Comments: 1

find A_n = ∫_0 ^1 (x^n /(ch(x))) dx .

$f i n d A_{n} = \int_{0}^{1} \frac{x^{n}}{c h (x)} d x .$

Question Number 37283 Answers: 0 Comments: 1

find ∫_0 ^∞ ((cosx)/(ch(x))) dx .

$f i n d \int_{0}^{\infty} \frac{c o s x}{c h (x)} d x .$

Question Number 37281 Answers: 0 Comments: 1

find a better approximation for the integrals 1) ∫_0 ^1 e^(−x^2 ) dx 2) ∫_1 ^(+∞) e^(−x^2 ) dx .

$f i n d a b e t t e r a p p r o x i m a t i o n f o r t h e$ $i n t e g r a l s$ $1) \int_{0}^{1} e^{- x^{2}} d x$ $2) \int_{1}^{+ \infty} e^{- x^{2}} d x .$

Question Number 37280 Answers: 0 Comments: 1

calculate ∫_0 ^6 (e^(x−[x]) /(1+e^x ))dx .

$c a l c u l a t e \int_{0}^{6} \frac{e^{x - [x]}}{1 + e^{x}} d x .$

Question Number 37279 Answers: 1 Comments: 1

cslculate ∫∫_([0,1]^2 ) (x−y)e^(−x−y) dxdy .

$c s l c u l a t e \int \int_{{[0, 1]}^{2}} (x - y) e^{- x - y} d x d y .$

Question Number 37278 Answers: 0 Comments: 1

calculate ∫∫_D x cos(x^2 +y^2 )dxdy with D={(x,y)∈R^2 / 0≤x≤1 and 1≤y≤3}

$c a l c u l a t e \int \int_{D} x c o s (x^{2} + y^{2}) d x d y$ $w i t h D = {(x, y) \in R^{2} / 0 ⩽ x ⩽ 1 a n d$ $1 ⩽ y ⩽ 3}$

Question Number 37276 Answers: 0 Comments: 0

calculate I_n =∫_0 ^4 (−1)^([x]) (x^n −x)dx

$c a l c u l a t e I_{n} = \int_{0}^{4} {(- 1)}^{[x]} (x^{n} - x) d x$

Question Number 37275 Answers: 0 Comments: 0

let A_n = ∫_0 ^(1/n) arctan(1+x^2 )dx 1) calculate A_n 2)find lim_(n→+∞) A_n .

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

Question Number 37272 Answers: 0 Comments: 0

let f(x)=cos(x−e^(−x) ) developp f at integr serie.

$l e t f (x) = c o s (x - e^{- x})$ $d e v e l o p p f a t i n t e g r s e r i e .$

Question Number 37271 Answers: 0 Comments: 2

find A_n =∫_1 ^2 ( 1 +(1/x) +(1/x^2 ) +...+(1/x^n ))^2 dx

$f i n d A_{n} = \int_{1}^{2} {(1 + \frac{1}{x} + \frac{1}{x^{2}} + . . . + \frac{1}{x^{n}})}^{2} d x$

Question Number 37270 Answers: 1 Comments: 0

find ∫_0 ^1 (((1−x^(n+1) )/(1−x)))^2 dx .

$f i n d \int_{0}^{1} {(\frac{1 - x^{n + 1}}{1 - x})}^{2} d x .$

Question Number 37258 Answers: 1 Comments: 0

∫ ((x^3 +1)/(√(x^2 +x))) dx = ?

$\int \frac{x^{3} + 1}{\sqrt{x^{2} + x}} d x = ?$

Question Number 37540 Answers: 1 Comments: 0

For x>1 , ∫ sin^(−1) (((2x)/(1+x^2 )))dx = ?

$For x > 1,$ $\int \sin^{- 1} (\frac{2 x}{1 + x^{2}}) d x = ?$

Question Number 37243 Answers: 0 Comments: 0

find f (t) =∫_0 ^∞ e^x ln(1+e^(−tx) )dx with t >0 . 2) let u_n = ∫_0 ^∞ e^x ln(1+e^(−nx) ) dx find lim_(n→+∞) u_n .

$f i n d f (t) = \int_{0}^{\infty} e^{x} l n (1 + e^{- t x}) d x w i t h t > 0 .$ $2) l e t u_{n} = \int_{0}^{\infty} e^{x} l n (1 + e^{- n x}) d x$ $f i n d {l i m}_{n \to + \infty} u_{n} .$

Question Number 37237 Answers: 1 Comments: 1

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

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

Question Number 37236 Answers: 0 Comments: 0

calculate ∫_0 ^(2π) ∣sin(((kt)/2))∣ dt with k integr and k≥3

$c a l c u l a t e \int_{0}^{2 π} ∣ s i n (\frac{k t}{2}) ∣ d t w i t h k i n t e g r$ $a n d k ⩾ 3$

Question Number 37235 Answers: 1 Comments: 0

calculate ∫_0 ^(π/2) (√(4sin^2 t +cos^2 (t))) dt

$c a l c u l a t e \int_{0}^{\frac{π}{2}} \sqrt{4 {s i n}^{2} t + {c o s}^{2} (t)} d t$

Question Number 37233 Answers: 0 Comments: 0

calculate ∫_(−∞) ^(+∞) (((1+ix)/(1−ix)))^(m−n) (dx/(1+x^2 )) dx with m and n integrs

$c a l c u l a t e$ $\int_{- \infty}^{+ \infty} {(\frac{1 + i x}{1 - i x})}^{m - n} \frac{d x}{1 + x^{2}} d x w i t h m a n d n$ $i n t e g r s$

Question Number 37225 Answers: 0 Comments: 0

let n≥2 and f : R_n [x]→R_2 [x] / f(p) =xp(1) +(x^2 −4)p(0) 1) prove that f is linear 2) find dim Kerf and dimIm(f)

$l e t n ⩾ 2 a n d f : R_{n} [x] \to R_{2} [x] /$ $f (p) = x p (1) + (x^{2} - 4) p (0)$ $1) p r o v e t h a t f i s l i n e a r$ $2) f i n d d i m K e r f a n d d i m I m (f)$

Pg 275 Pg 276 Pg 277 Pg 278 Pg 279 Pg 280 Pg 281 Pg 282 Pg 283 Pg 284

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