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IntegrationQuestion and Answers: Page 240

Question Number 56698 Answers: 0 Comments: 2

find the value of ∫_0 ^∞ ((sin(x^2 ))/(x^4 +4))dx

$f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{s i n (x^{2})}{x^{4} + 4} d x$

Question Number 56629 Answers: 0 Comments: 2

1) calculate I =∫_(−∞) ^(+∞) (dx/(x^2 −i)) and J =∫_(−∞) ^(+∞) (dx/(x^2 −i)) 2) find the value of ∫_(−∞) ^(+∞) (dx/(x^4 +1))

$1) c a l c u l a t e I = \int_{- \infty}^{+ \infty} \frac{d x}{x^{2} - i} a n d J = \int_{- \infty}^{+ \infty} \frac{d x}{x^{2} - i}$ $2) f i n d t h e v a l u e o f \int_{- \infty}^{+ \infty} \frac{d x}{x^{4} + 1}$

Question Number 56523 Answers: 0 Comments: 2

∫x(√(3x^3 +2)) dx=?

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

Question Number 56383 Answers: 2 Comments: 4

Question Number 56329 Answers: 0 Comments: 1

1)calculate A_n =∫_(1/n) ^1 ((ln(1+x^2 ))/(1+x^2 ))dx with n integr and n≥1 2) find lim_(n→+∞) A_n 3) study the convergence of Σ A_n

$1) c a l c u l a t e A_{n} = \int_{\frac{1}{n}}^{1} \frac{l n (1 + x^{2})}{1 + x^{2}} d x w i t h n i n t e g r a n d n ⩾ 1$ $2) f i n d {l i m}_{n \to + \infty} A_{n}$ $3) s t u d y t h e c o n v e r g e n c e o f Σ A_{n}$

Question Number 56345 Answers: 0 Comments: 1

let f(a) =∫_0 ^∞ (dx/(x^n +a^n )) with n integr ≥2 and a>0 1) calculate f(a) intems of a 2) let g(a) =∫_0 ^∞ (dx/((x^n +a^n )^2 )) calculate g(a) interms of a 3) find the values of integrals ∫_0 ^∞ (dx/(x^8 +16)) and ∫_0 ^∞ (dx/((x^8 +16)^2 ))

$l e t f (a) = \int_{0}^{\infty} \frac{d x}{x^{n} + a^{n}} w i t h n i n t e g r ⩾ 2 a n d a > 0$ $1) c a l c u l a t e f (a) i n t e m s o f a$ $2) l e t g (a) = \int_{0}^{\infty} \frac{d x}{{(x^{n} + a^{n})}^{2}} c a l c u l a t e g (a) i n t e r m s o f a$ $3) f i n d t h e v a l u e s o f i n t e g r a l s \int_{0}^{\infty} \frac{d x}{x^{8} + 16} a n d \int_{0}^{\infty} \frac{d x}{{(x^{8} + 16)}^{2}}$

Question Number 56311 Answers: 0 Comments: 1

let f(x) =∫_0 ^∞ ((cos(xt))/(x^2 +t^2 )) dt with x>0 1) find f(x) 2) find the values of ∫_0 ^∞ ((cos(t))/(1+t^2 ))dt and ∫_0 ^∞ ((cos(2t))/(4+t^2 ))dt 3) let U_n =∫_0 ^∞ ((cos(nt))/(n^2 +t^2 ))dt find lim_(n→+∞) U_n and study the convergenge of Σ U_n and Σ U_n ^2

$l e t f (x) = \int_{0}^{\infty} \frac{c o s (x t)}{x^{2} + t^{2}} d t w i t h x > 0$ $1) f i n d f (x)$ $2) f i n d t h e v a l u e s o f \int_{0}^{\infty} \frac{c o s (t)}{1 + t^{2}} d t a n d \int_{0}^{\infty} \frac{c o s (2 t)}{4 + t^{2}} d t$ $3) l e t U_{n} = \int_{0}^{\infty} \frac{c o s (n t)}{n^{2} + t^{2}} d t f i n d {l i m}_{n \to + \infty} U_{n} a n d s t u d y t h e c o n v e r g e n g e o f$ $Σ U_{n} a n d Σ U_{n}^{2}$

Question Number 56310 Answers: 0 Comments: 2

let f(x)=∫_(−∞) ^(+∞) cos(t^2 +xt +3)dt with x>0 1) find f(x) 2) calculate ∫_1 ^4 f(x)dx and ∫_1 ^(+∞) f(x)dx

$l e t f (x) = \int_{- \infty}^{+ \infty} c o s (t^{2} + x t + 3) d t w i t h x > 0$ $1) f i n d f (x)$ $2) c a l c u l a t e \int_{1}^{4} f (x) d x a n d \int_{1}^{+ \infty} f (x) d x$

Question Number 56280 Answers: 2 Comments: 2

Evaluate : 1) ((∫_0 ^( 1_ ) (1−(1−x^2 )^(100) )^(201) .xdx)/(∫_0 ^( 1) (1−(1−x^2 )^(100) )^(202) .xdx)) = ? 2) ((∫_0 ^( 1) (1−x^(200) )^(201) dx)/(∫_0 ^( 1) (1−x^(200) )^(202) dx)) = ?

$E v a l u a t e :$ $1) \frac{\int_{0}^{1_{}} {(1 - {(1 - x^{2})}^{100})}^{201} . x d x}{\int_{0}^{1} {(1 - {(1 - x^{2})}^{100})}^{202} . x d x} = ?$ $2) \frac{\int_{0}^{1} {(1 - x^{200})}^{201} d x}{\int_{0}^{1} {(1 - x^{200})}^{202} d x} = ?$