Question and Answers Forum

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) .

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

Pg 283 Pg 284 Pg 285 Pg 286 Pg 287 Pg 288 Pg 289 Pg 290 Pg 291 Pg 292

Contact: info@tinkutara.com