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IntegrationQuestion and Answers: Page 275

Question Number 39967 Answers: 0 Comments: 4

1) decompose inside C(x) the fraction F(x)= (3/(4+x^4 )) 2) find ∫_(−∞) ^(+∞) (dx/(x−z)) with z from C 3) find the value of ∫_(−∞) ^(+∞) ((3dx)/(4+x^4 )) .

$1) d e c o m p o s e i n s i d e C (x) t h e f r a c t i o n$ $F (x) = \frac{3}{4 + x^{4}}$ $2) f i n d \int_{- \infty}^{+ \infty} \frac{d x}{x - z} w i t h z f r o m C$ $3) f i n d t h e v a l u e o f \int_{- \infty}^{+ \infty} \frac{3 d x}{4 + x^{4}} .$

Question Number 39840 Answers: 0 Comments: 1

calculate lim_(x→0) ∫_(x+1) ^(x^2 +1) ln(1+t) e^(−t) dt

$c a l c u l a t e {l i m}_{x \to 0} \int_{x + 1}^{x^{2} + 1} l n (1 + t) e^{- t} d t$

Question Number 39838 Answers: 0 Comments: 1

find lim_(ξ→0) ∫_0 ^1 (dx/((√(1+ξx^2 ))−(√(1−ξx^2 ))))

$f i n d {l i m}_{ξ \to 0} \int_{0}^{1} \frac{d x}{\sqrt{1 + ξ x^{2}} - \sqrt{1 - ξ x^{2}}}$

Question Number 39836 Answers: 0 Comments: 0

calculate ∫_0 ^(+∞) ((ln(1+ix^2 ))/(2+x^2 ))dx

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

Question Number 39834 Answers: 1 Comments: 0

calculate ∫_0 ^(π/6) ∣ cos(2x)−cos(3x)∣dx

$c a l c u l a t e \int_{0}^{\frac{π}{6}} ∣ c o s (2 x) - c o s (3 x) ∣ d x$

Question Number 39833 Answers: 2 Comments: 1

find ∫ ((ln(x+(√(x^2 −1))))/(√(x^2 −1))) dx 2) calculate ∫_2 ^5 ((ln(x+(√(x^2 −1)))/(√(x^2 −1)))dx

$f i n d \int \frac{l n (x + \sqrt{x^{2} - 1})}{\sqrt{x^{2} - 1}} d x$ $2) c a l c u l a t e \int_{2}^{5} \frac{l n (x + \sqrt{x^{2} - 1}}{\sqrt{x^{2} - 1}} d x$

Question Number 40139 Answers: 0 Comments: 3

let I_n = ∫_0 ^1 x^n (√(1−x)) dx 1) calculate I_0 and I_1 2) prove that ∀n∈ N^★ (3+2n) I_n =2n I_(n−1) 3) find I_n interms of n

$l e t I_{n} = \int_{0}^{1} x^{n} \sqrt{1 - x} d x$ $1) c a l c u l a t e I_{0} a n d I_{1}$ $2) p r o v e t h a t \forall n \in N^{★} (3 + 2 n) I_{n} = 2 n I_{n - 1}$ $3) f i n d I_{n} i n t e r m s o f n$

Question Number 39787 Answers: 0 Comments: 2

calculste I_λ = ∫_(−∞) ^(+∞) ((cos(λx^n ))/(1+x^2 )) dx with λ from R and n integr natural 2) find the vslue of ∫_(−∞) ^(+∞) ((cos(3 x^9 ))/(1+x^2 )) dx .

$c a l c u l s t e I_{λ} = \int_{- \infty}^{+ \infty} \frac{c o s (λ x^{n})}{1 + x^{2}} d x w i t h$ $λ f r o m R a n d n i n t e g r n a t u r a l$ $2) f i n d t h e v s l u e o f \int_{- \infty}^{+ \infty} \frac{c o s (3 x^{9})}{1 + x^{2}} d x .$

Question Number 39712 Answers: 1 Comments: 3

calculate ∫_(−∞) ^(+∞) ((cos(x^n ) +sin(x^n ))/((x^2 +9)^n )) dx

$c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{c o s (x^{n}) + s i n (x^{n})}{{(x^{2} + 9)}^{n}} d x$

Question Number 39711 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) (x^n /((1+x^2 )^n )) dx with n natral integr

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

Question Number 39706 Answers: 0 Comments: 0

Question Number 39660 Answers: 0 Comments: 2

let S_n = ∫_0 ^n ((x(−1)^([x]) )/((x+1 −[x])^3 ))dx 1) calculate S_n 2) find lim_(n→+∞) S_n

$l e t S_{n} = \int_{0}^{n} \frac{x {(- 1)}^{[x]}}{{(x + 1 - [x])}^{3}} d x$ $1) c a l c u l a t e S_{n}$ $2) f i n d {l i m}_{n \to + \infty} S_{n}$

Question Number 39633 Answers: 0 Comments: 3

find the value of f(x) = ∫_0 ^π ln(x^2 −2x cosθ +1)dθ with x fromR.

$f i n d t h e v a l u e o f$ $f (x) = \int_{0}^{π} l n (x^{2} - 2 x c o s θ + 1) d θ w i t h x f r o m R .$

Question Number 39443 Answers: 1 Comments: 3

lim_(n→∞) [ (1/(n^2 +1))+ (2/(n^2 +2))+ (3/(n^2 +3))+ ....+(1/(n+1))] = ?

$\lim_{n \to \infty} [\frac{1}{n^{2} + 1} + \frac{2}{n^{2} + 2} + \frac{3}{n^{2} + 3} + . . . . + \frac{1}{n + 1}] = ?$

Question Number 39441 Answers: 0 Comments: 2

∫_(1/4) ^( 4) (1/x) sin (x−(1/x))dx = ?

$\int_{\frac{1}{4}}^{4} \frac{1}{x} \sin (x - \frac{1}{x}) d x = ?$

Question Number 39440 Answers: 1 Comments: 0

f(x)= ∫_0 ^( x_ ) e^(t ) (((1+sin t)/(1+cos t))) dt. Then f((π/3))×f(((2π)/3)) = ?

$f (x) = \int_{0}^{x_{}} e^{t} (\frac{1 + \sin t}{1 + \cos t}) d t .$ $T hen f (\frac{π}{3}) \times f (\frac{2 π}{3}) = ?$

Question Number 39477 Answers: 1 Comments: 3

∫2^x 3^(2x) dx=?

$\int 2^{x} 3^{2 x} dx = ?$

Question Number 39431 Answers: 1 Comments: 1

∫_0 ^(2π) e^(x/2) sin ((x/2)+(π/4))dx = ?

$\int_{0}^{2 π} e^{\frac{x}{2}} \sin (\frac{x}{2} + \frac{π}{4}) d x = ?$

Question Number 39483 Answers: 0 Comments: 3

find f(t)= ∫_0 ^1 ((ln(1+xt))/(1+x^2 )) dx .

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

Question Number 39389 Answers: 0 Comments: 2

calculate F(x) = ∫_0 ^∞ (dt/(1+(1+x(1+t^2 ))^2 ))

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

Question Number 39386 Answers: 1 Comments: 1

find the value of ∫_0 ^1 ((ln(1+x))/(1+x^2 ))dx

$f i n d t h e v a l u e o f \int_{0}^{1} \frac{l n (1 + x)}{1 + x^{2}} d x$

Question Number 39384 Answers: 2 Comments: 0

The values of a for which y= ax^2 +ax+(1/(24)) and x = ay^2 +ay+(1/(24)) touch each other are 1) (2/3) 2) (3/2) 3) ((13+(√(601)))/(12)) 4) ((13−(√(601)))/(12)).

$The values of a for which y = a x^{2} + a x + \frac{1}{24}$ $a n d x = {a y}^{2} + a y + \frac{1}{24} t o u c h e a c h o t h e r$ $a r e$ $1) \frac{2}{3} 2) \frac{3}{2}$ $3) \frac{13 + \sqrt{601}}{12} 4) \frac{13 - \sqrt{601}}{12} .$

Question Number 39383 Answers: 1 Comments: 1

calculate ∫_0 ^(π/3) ((sinxdx)/(cosx(2+ln(cosx))) .

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

Question Number 39382 Answers: 1 Comments: 0

Question Number 39381 Answers: 1 Comments: 0

Question Number 39379 Answers: 1 Comments: 6

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