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IntegrationQuestion and Answers: Page 286

Question Number 36415 Answers: 0 Comments: 1

calculate I = ∫_0 ^(π/2) (x^3 +x)cos^2 xdx and J = ∫_0 ^(π/2) (x^3 +x)sin^2 xdx cslculate I and J .

$c a l c u l a t e I = \int_{0}^{\frac{π}{2}} (x^{3} + x) {c o s}^{2} x d x a n d$ $J = \int_{0}^{\frac{π}{2}} (x^{3} + x) {s i n}^{2} x d x$ $c s l c u l a t e I a n d J .$

Question Number 36413 Answers: 0 Comments: 1

let I_n = ∫_0 ^1 x^n (√(3+x))dx 1)calculate lim_(n→+∞) I_n 2) calculate lim_(n→+∞) n I_n

$l e t I_{n} = \int_{0}^{1} x^{n} \sqrt{3 + x} d x$ $1) c a l c u l a t e {l i m}_{n \to + \infty} I_{n}$ $2) c a l c u l a t e {l i m}_{n \to + \infty} n I_{n}$

Question Number 36412 Answers: 1 Comments: 1

calculate I_λ =∫_0 ^λ e^(−x) ln(1+e^x )dx

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

Question Number 36411 Answers: 0 Comments: 0

calculate ∫_1 ^3 ((x−1)/(∣x^2 −2x∣ +1))dx

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

Question Number 36410 Answers: 0 Comments: 1

find the value of I_n = ∫_0 ^1 x^n (√(1−x))dx

$f i n d t h e v a l u e o f I_{n} = \int_{0}^{1} x^{n} \sqrt{1 - x} d x$

Question Number 36406 Answers: 2 Comments: 1

find the values of I = ∫_0 ^π cos^4 dx and J = ∫_0 ^π sin^4 dx .

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

Question Number 36397 Answers: 2 Comments: 0

find I = ∫_1 ^2 (dx/(x(√(x+1)) +(x+1)(√x)))

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

Question Number 36394 Answers: 0 Comments: 0

let f(x)=artanx find L(f(x)) L mean laplace trsnsform.

$l e t f (x) = a r t a n x f i n d L (f (x))$ $L m e a n l a p l a c e t r s n s f o r m .$

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) .

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

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