Question and Answers Forum

All Questions Topic List

IntegrationQuestion and Answers: Page 194

Question Number 80925 Answers: 0 Comments: 1

∫_(−∞) ^∞ ((cos(x))/(1+x^2 )) dx =(π/e)

$\int_{- \infty}^{\infty} \frac{c o s (x)}{1 + x^{2}} d x = \frac{π}{e}$

Question Number 80924 Answers: 1 Comments: 3

show that ∫_0 ^∞ (x^((π/5)−1) /(1+x^(2π) )) dx =φ

$s h o w t h a t$ $\int_{0}^{\infty} \frac{x^{\frac{π}{5} - 1}}{1 + x^{2 π}} d x = ϕ$

Question Number 80921 Answers: 0 Comments: 2

∫_0 ^(π/2) ((xdx)/(sin x+cos x)) = ?

$\underset{0}{\int^{\frac{π}{2}}} \frac{x d x}{\sin x + \cos x} = ?$

Question Number 80914 Answers: 0 Comments: 0

(1) Integrate F(x, y) = x^2 over the region bounded by y = x^2 , x = 2 and x = 1 (2) Integrate G(x, y) = x^2 + y^2 over the region bounded by the triangle x = y, y = 1 and y = 0

$(1)$ $Integrate F (x, y) = x^{2} over the region bounded by y = x^{2},$ $x = 2 and x = 1$ $(2)$ $Integrate G (x, y) = x^{2} + y^{2} over the region bounded by the$ $triangle x = y, y = 1 and y = 0$

Question Number 80882 Answers: 1 Comments: 4

Question Number 80846 Answers: 1 Comments: 4

Question Number 80788 Answers: 0 Comments: 0

Question Number 80770 Answers: 1 Comments: 1

∫x^2 +3x dx=..

$\int x^{2} + 3 x dx = . .$

Question Number 80764 Answers: 1 Comments: 0

show that ∫_0 ^∞ x arctanh(e^(−αx) )dx=((7ζ(3))/(8α^2 ))

$s h o w t h a t$ $\int_{0}^{\infty} x a r c t a n h (e^{- α x}) d x = \frac{7 ζ (3)}{8 α^{2}}$

Question Number 80752 Answers: 1 Comments: 1

Question Number 80612 Answers: 0 Comments: 3

Ψ(x)=∫_1 ^x (1/(√(1−e^t ))) dt ∀x∈R prove that Ψ(x)=2ln(((1−(√(1−e^x )))/(1−(√(1−e)))))−x+1

$Ψ (x) = \int_{1}^{x} \frac{1}{\sqrt{1 - e^{t}}} d t \forall x \in R$ $p r o v e t h a t$ $Ψ (x) = 2 l n (\frac{1 - \sqrt{1 - e^{x}}}{1 - \sqrt{1 - e}}) - x + 1$

Question Number 80485 Answers: 0 Comments: 1

what is the king rule?

$w h a t i s t h e k i n g r u l e ?$

Question Number 80452 Answers: 0 Comments: 1

find ∫_(−∞) ^(+∞) ((cos(2x^2 +1))/(x^4 −x^2 +3))dx

$f i n d \int_{- \infty}^{+ \infty} \frac{c o s (2 x^{2} + 1)}{x^{4} - x^{2} + 3} d x$

Question Number 80451 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((cos(πx))/((x^2 +3)^2 ))dx

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

Question Number 80432 Answers: 0 Comments: 7

Question Number 80416 Answers: 1 Comments: 0

∫_0 ^(π/2) ((xcos x)/((1+sin x)^2 )) dx ?

$\underset{0}{\int^{\frac{π}{2}}} \frac{x \cos x}{{(1 + \sin x)}^{2}} d x ?$

Question Number 80397 Answers: 0 Comments: 3

show that ∫_0 ^(π/2) ∫_0 ^∞ (1/((x^π )^(1/y) +1)) dx dy =2c whrre c denote tha catalan^, s constant

$s h o w t h a t$ $\int_{0}^{\frac{π}{2}} \int_{0}^{\infty} \frac{1}{\sqrt[y]{x^{π}} + 1} d x d y = 2 c$ $w h r r e c d e n o t e t h a {c a t a l a n}^{,} s c o n s t a n t$

Question Number 80369 Answers: 0 Comments: 1

Question Number 80334 Answers: 0 Comments: 1

let f∈L^1 (R) let u_n = ∫_a ^b f(t)sin(nt)dt , v_n =∫_a ^b ((f(t))/t)sin(nt) 1)Prove that lim_(n→∞) u_n =0 2)Deduce in term of a,b,f(0) the value of lim_(n→∞) v_n

$l e t f \in L^{1} (R)$ $l e t u_{n} = \int_{a}^{b} f (t) s i n (n t) d t, v_{n} = \int_{a}^{b} \frac{f (t)}{t} s i n (n t)$ $1) P r o v e t h a t \lim_{n \to \infty} u_{n} = 0$ $2) D e d u c e i n t e r m o f a, b, f (0) t h e v a l u e o f \lim_{n \to \infty} v_{n}$