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IntegrationQuestion and Answers: Page 289

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)

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

Question Number 36180 Answers: 1 Comments: 1

calculate ∫_0 ^1 ((ln(t))/((1+t)^2 ))dt

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

Question Number 36167 Answers: 0 Comments: 2

let give I = ∫_0 ^∞ (dx/((x^2 +i)^2 )) 1) extract Re(I) and Im(I) 2) find the value of I 3) calculate Re(I) and Im(I) .

$l e t g i v e I = \int_{0}^{\infty} \frac{d x}{{(x^{2} + i)}^{2}}$ $1) e x t r a c t R e (I) a n d I m (I)$ $2) f i n d t h e v a l u e o f I$ $3) c a l c u l a t e R e (I) a n d I m (I) .$

Question Number 36057 Answers: 2 Comments: 1

find the value of ∫_0 ^(π/4) ((cosx)/(sinx +tanx))dx

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

Question Number 36056 Answers: 1 Comments: 2

calculate ∫_(−∞) ^(+∞) ((2x)/((x^2 +mx +1)^2 ))dx with ∣m∣<2

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

Question Number 36031 Answers: 0 Comments: 0

Q. Evaluate: ∫_(∫xyzdxdydz) ^(∫zyxdzdydx) ∫_((d/dx)(x^(sin x) )) ^((d/dx)(x^(cos x) )) ∫_(lim_(x→0) ((−x^2 +2)/x)) ^(lim_(x→0) ((x^2 −2)/x)) ∫_0 ^∞ w^(1−x) x^(1−y) y^(1−z) z^(1−w) dwdxdydz

$Q . Evaluate : \int_{\int xyzdxdydz}^{\int zyxdzdydx} \int_{\frac{d}{dx} (x^{\sin x})}^{\frac{d}{dx} (x^{\cos x})} \int_{\lim_{x \to 0} \frac{- x^{2} + 2}{x}}^{\lim_{x \to 0} \frac{x^{2} - 2}{x}} \int_{0}^{\infty} w^{1 - x} x^{1 - y} y^{1 - z} z^{1 - w} dwdxdydz$

Question Number 36009 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((xdx)/((2x+1+i)^3 )) with i^2 =−1 .

$c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{x d x}{{(2 x + 1 + i)}^{3}} w i t h i^{2} = - 1 .$

Question Number 35990 Answers: 0 Comments: 2

calculate ∫_2 ^5 ((xdx)/(2x+1 +(√(x−1))))

$c a l c u l a t e \int_{2}^{5} \frac{x d x}{2 x + 1 + \sqrt{x - 1}}$

Question Number 35983 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((2(√t) +1)/(t^5 +3))dt .

$c a l c u l a t e \int_{0}^{\infty} \frac{2 \sqrt{t} + 1}{t^{5} + 3} d t .$

Question Number 35982 Answers: 0 Comments: 0

let f(t) =∫_0 ^∞ e^(−arctsn( 1+tx^2 )) dx with t from R 1) calculate f^′ (t) 2) find a simple form of f(t) .

$l e t f (t) = \int_{0}^{\infty} e^{- a r c t s n (1 + {t x}^{2})} d x w i t h t f r o m R$ $1) c a l c u l a t e f^{^{'}} (t)$ $2) f i n d a s i m p l e f o r m o f f (t) .$

Question Number 35949 Answers: 1 Comments: 1

∫_0 ^( α) ((tan θ)/(√(a^2 cos^2 θ−b^2 sin^2 θ))) dθ = ?

$\int_{0}^{α} \frac{\tan θ}{\sqrt{a^{2} \cos^{2} θ - b^{2} \sin^{2} θ}} d θ = ?$

Question Number 35920 Answers: 1 Comments: 1

∫ ((e^(2x) +1)/(2e^x −1)) dx = ?

$\int \frac{e^{2 x} + 1}{2 e^{x} - 1} d x = ?$

Question Number 35909 Answers: 1 Comments: 4

∫((7x−6)/((x^2 +25)(√((x−3)^2 +4)))) dx = ?

$\int \frac{7 x - 6}{(x^{2} + 25) \sqrt{{(x - 3)}^{2} + 4}} d x = ?$

Question Number 35832 Answers: 1 Comments: 3

find the value of f(λ) = ∫_(−a) ^a (dx/((λ +_ x^2 )^(3/2) )) λ∈R .

$f i n d t h e v a l u e o f f (λ) = \int_{- a}^{a} \frac{d x}{{(λ +_{} x^{2})}^{\frac{3}{2}}}$ $λ \in R .$

Question Number 35821 Answers: 0 Comments: 4

let f(t) = ∫_0 ^∞ ((e^(−ax) −e^(−bx) )/x^2 ) e^(−tx^2 ) dx with t>0 1) calculate f^′ (t) 2)find a simple form of f(t) 3) find the value of ∫_0 ^∞ ((e^(−2x) −e^(−x) )/x^2 ) e^(−3x^2 ) dx

$l e t f (t) = \int_{0}^{\infty} \frac{e^{- a x} - e^{- b x}}{x^{2}} e^{- {t x}^{2}} d x w i t h t > 0$ $1) c a l c u l a t e f^{^{'}} (t)$ $2) f i n d a s i m p l e f o r m o f f (t)$ $3) f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{e^{- 2 x} - e^{- x}}{x^{2}} e^{- 3 x^{2}} d x$

Question Number 35732 Answers: 1 Comments: 1

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