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IntegrationQuestion and Answers: Page 4

Question Number 217683 Answers: 0 Comments: 0

Prove:∫_0 ^1 (√((((√(K^2 +36K′^2 ))+6K^′ )/(K^2 +36K^(′2) )) ))(dk/( (√k)(1−k^2 )^(2/3) ))=(√π)((√2)−(√((4−2(√2))/3)))

$Prove : \int_{0}^{1} \sqrt{\frac{\sqrt{K^{2} + 36 K^{' 2}} + 6 K^{^{'}}}{K^{2} + 36 K^{^{'} 2}}} \frac{d k}{\sqrt{k} {(1 - k^{2})}^{\frac{2}{3}}} = \sqrt{π} (\sqrt{2} - \sqrt{\frac{4 - 2 \sqrt{2}}{3}})$

Question Number 217685 Answers: 0 Comments: 0

Question Number 217626 Answers: 1 Comments: 0

lim_( λ→0) ∫_λ ^( 2λ) (( e^(2t ) )/t) dt = ?

$\lim_{λ \to 0} \int_{λ}^{2 λ} \frac{e^{2 t}}{t} d t = ?$

Question Number 217441 Answers: 2 Comments: 0

∫_0 ^1 ((ln^3 (1−x))/x^3 ) dx=?

$\int_{0}^{1} \frac{\ln^{3} (1 - x)}{x^{3}} d x = ?$

Question Number 217431 Answers: 2 Comments: 0

Question Number 217423 Answers: 1 Comments: 0

Question Number 217408 Answers: 1 Comments: 0

l∫sin 7xdx

$l \int \sin 7 x d x$

Question Number 217356 Answers: 1 Comments: 0

Question Number 217290 Answers: 4 Comments: 0

∫_0 ^( 1) ((ln^2 (1−x))/x^2 ) dx= ?

$\int_{0}^{1} \frac{\ln^{2} (1 - x)}{x^{2}} d x = ?$

Question Number 217289 Answers: 1 Comments: 1

∫_0 ^1 sin^(−1) (1/( (√(1+x−x^2 )))) dx=?

$\underset{0}{\int^{1}} \sin^{- 1} \frac{1}{\sqrt{1 + x - x^{2}}} d x = ?$

Question Number 217255 Answers: 1 Comments: 0

∫_(−∞) ^(+∞) e^(−(x^2 /2)) dx=(√(2π)),∫_(−∞) ^(+∞) e^(−(x^2 /2)+x) dx.

$\int_{- \infty}^{+ \infty} e^{- \frac{x^{2}}{2}} d x = \sqrt{2 π}, \int_{- \infty}^{+ \infty} e^{- \frac{x^{2}}{2} + x} d x .$

Question Number 217219 Answers: 1 Comments: 0

calculate determinant ((( L ( ∫_1 ^( ∞) (( e^( −tx) )/x)dx ) =_(transfom) ^(laplace) ? ; t>0 )))

$c a l c u l a t e$ $\begin{matrix} L (\int_{1}^{\infty} \frac{e^{- t x}}{x} d x) \underset{transfom}{\overset{laplace}{=}} ?; t > 0 \end{matrix}$

Question Number 217211 Answers: 1 Comments: 0

a nice one: prove ∫_0 ^1 (√(−((ln t)/t))) dt=(√(2π))

$a nice one :$ $prove \underset{0}{\int^{1}} \sqrt{- \frac{\ln t}{t}} d t = \sqrt{2 π}$

Question Number 217122 Answers: 1 Comments: 0

∫ ((√(cos 2x))/(cos x)) dx =?

$\int \frac{\sqrt{\cos 2 x}}{\cos x} dx = ?$

Question Number 216990 Answers: 2 Comments: 0

(1) ∫(sec^2 x∙(√(tan x)))dx=?

$(1) \int (\sec^{2} x \cdot \sqrt{\tan x}) d x = ?$

Question Number 216886 Answers: 0 Comments: 1

Evaluate ((Σ_(k=1) ^(10) (∫_0 ^k (4u+1)du))/(5^2 Σ_(n=1) ^∞ (1/2)(Σ_(n=2) ^∞ (2/(m^2 +2m)))^(n−1) ))∫_(sin^(−1) (((−(√2))/2))) ^((π/2)cos(π/2)) (((1−secθsinθ)/((tanθ+cotθ)/(ϱ^θ −ϱ^(πi) ))))dθ

$E v a l u a t e \frac{\underset{k = 1}{\sum^{10}} (\int_{0}^{k} (4 u + 1) d u)}{5^{2} \underset{n = 1}{\sum^{\infty}} \frac{1}{2} {(\underset{n = 2}{\sum^{\infty}} \frac{2}{m^{2} + 2 m})}^{n - 1}} \int_{{s i n}^{- 1} (\frac{- \sqrt{2}}{2})}^{\frac{π}{2} c o s \frac{π}{2}} (\frac{1 - s e c θ s i n θ}{\frac{t a n θ + c o t θ}{ϱ^{θ} - ϱ^{π i}}}) d θ$

Question Number 216819 Answers: 0 Comments: 0

Prove:∫_(0 ) ^1 ((K(x))/( (√(3−x))))dx=(1/(96π(√3)))×Γ((1/(24)))Γ((3/(24)))Γ((7/(24)))Γ(((11)/(24)))

$Prove : \int_{0}^{1} \frac{K (x)}{\sqrt{3 - x}} d x = \frac{1}{96 π \sqrt{3}} \times Γ (\frac{1}{24}) Γ (\frac{3}{24}) Γ (\frac{7}{24}) Γ (\frac{11}{24})$

Question Number 216799 Answers: 1 Comments: 1

Question Number 216776 Answers: 1 Comments: 0

Question Number 216774 Answers: 1 Comments: 0

find ∫ ((tan^2 (x) )/(1+sec^4 (x))) .dx

$f i n d \int \frac{{t a n}^{2} (x)}{1 + {s e c}^{4} (x)} . d x$

Question Number 216772 Answers: 1 Comments: 0

find ∫((tan^2 (x) )/(1−sec^4 (x))) .dx

$f i n d \int \frac{{t a n}^{2} (x)}{1 - {s e c}^{4} (x)} . d x$

Question Number 216754 Answers: 2 Comments: 0

∫_( 0) ^( 1) ((x ln^2 (x))/(1 + x^2 )) dx

$\int_{0}^{1} \frac{x \ln^{2} (x)}{1 + x^{2}} dx$

Question Number 216742 Answers: 1 Comments: 0

(1/2)∫_( 0) ^( 1) ((ln(a − 1))/a) da

$\frac{1}{2} \int_{0}^{1} \frac{\ln (a - 1)}{a} da$

Question Number 216715 Answers: 2 Comments: 0

Find ∫((Sin(((5x )/(2 ))) )/(Sin(((x )/(2 ))) )) .dx

$F i n d \int \frac{S i n (\frac{5 x}{2})}{S i n (\frac{x}{2})} . d x$

Question Number 216618 Answers: 2 Comments: 0

∫_( 0) ^( 2π) (√(1 − cos^2 x)) dx Is the answer 0 or 4????

$\int_{0}^{2 π} \sqrt{1 - \cos^{2} x} dx$ $Is the answer 0 or 4 ? ? ? ?$

Question Number 216613 Answers: 0 Comments: 1

∫_a ^( x) ((1−bln (x/a))/( (√(1−(1−bln (x/a))^2 )))) dx

$\int_{a}^{x} \frac{1 - b \ln \frac{x}{a}}{\sqrt{1 - {(1 - b \ln \frac{x}{a})}^{2}}} d x$

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10

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