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IntegrationQuestion and Answers: Page 231

Question Number 62335 Answers: 0 Comments: 2

1) calculate f(x,y) =∫_0 ^∞ ((e^(−xt) cos(yt))/(√t)) dt and g(x,y) =∫_0 ^∞ ((e^(−xt) sin(yt))/(√t)) dt with x>0 and y>0 2) find the values of ∫_0 ^∞ ((e^(−2t) cos(t))/(√t)) dt and ∫_0 ^∞ ((e^(−t) cos(2t))/(√t)) dt

$1) c a l c u l a t e f (x, y) = \int_{0}^{\infty} \frac{e^{- x t} c o s (y t)}{\sqrt{t}} d t a n d g (x, y) = \int_{0}^{\infty} \frac{e^{- x t} s i n (y t)}{\sqrt{t}} d t$ $w i t h x > 0 a n d y > 0$ $2) f i n d t h e v a l u e s o f \int_{0}^{\infty} \frac{e^{- 2 t} c o s (t)}{\sqrt{t}} d t a n d \int_{0}^{\infty} \frac{e^{- t} c o s (2 t)}{\sqrt{t}} d t$

Question Number 62330 Answers: 1 Comments: 1

find the value of ∫_0 ^∞ (t^(a−1) /((1+t)^2 ))dt with 0<a<1

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

Question Number 62274 Answers: 1 Comments: 4

∫_0 ^∞ e^(−x^2 ) dx

$\underset{0}{\int^{\infty}} e^{- x^{2}} d x$

Question Number 62266 Answers: 1 Comments: 1

∫((2sin(x)+3cos(x))/(3sin(x)+4cos(x)))dx

$\int \frac{2 s i n (x) + 3 c o s (x)}{3 s i n (x) + 4 c o s (x)} d x$

Question Number 62262 Answers: 1 Comments: 1

find the value of I =∫_0 ^∞ ((e^(−t) sint)/(√t))dt and J =∫_0 ^∞ ((e^(−t) cos(t))/(√t))dt ,study first the convergence.

$f i n d t h e v a l u e o f$ $I = \int_{0}^{\infty} \frac{e^{- t} s i n t}{\sqrt{t}} d t a n d J = \int_{0}^{\infty} \frac{e^{- t} c o s (t)}{\sqrt{t}} d t, s t u d y f i r s t t h e c o n v e r g e n c e .$

Question Number 62252 Answers: 0 Comments: 1

∫ln(x+1)/(x^2 −x+1) limit ={ 0>2}

$\int \ln (x + 1) / (x^{2} - x + 1)$ $limit = {0 > 2}$

Question Number 62251 Answers: 0 Comments: 1

∫(x^2 −4)^(1/2) dx trig substitution only

$\int {(x^{2} - 4)}^{1 / 2} dx$ $trig substitution only$

Question Number 62232 Answers: 0 Comments: 4

Question Number 62227 Answers: 0 Comments: 3

1.∫(√(1+x+x^2 +x^3 ))dx=? 2.∫ ((√(1−tgx))/(sinx)) dx=? 3.∫ e^x .ln(1+(√(1+x^2 )))dx=? 4.∫ ((sinx)/(1+sinx+sin2x)) dx=?

$1 . \int \sqrt{1 + x + x^{2} + x^{3}} dx = ?$ $2 . \int \frac{\sqrt{1 - tgx}}{sinx} dx = ?$ $3 . \int e^{x} . \ln (1 + \sqrt{1 + x^{2}}) dx = ?$ $4 . \int \frac{sinx}{1 + sinx + \sin 2 x} dx = ?$

Question Number 62220 Answers: 0 Comments: 2

let f(x) =∫_0 ^∞ (t^2 /(x^6 +t^6 )) dt with x>0 1) calculate f(x) 2) calculate g(x) =∫_0 ^∞ (t^2 /((x^6 +t^6 )^2 ))dt 3) find values of integrals ∫_0 ^∞ (t^2 /(t^6 +8))dt and ∫_0 ^∞ (t^2 /((t^6 +8)^2 ))dt .

$l e t f (x) = \int_{0}^{\infty} \frac{t^{2}}{x^{6} + t^{6}} d t w i t h x > 0$ $1) c a l c u l a t e f (x)$ $2) c a l c u l a t e g (x) = \int_{0}^{\infty} \frac{t^{2}}{{(x^{6} + t^{6})}^{2}} d t$ $3) f i n d v a l u e s o f i n t e g r a l s \int_{0}^{\infty} \frac{t^{2}}{t^{6} + 8} d t a n d \int_{0}^{\infty} \frac{t^{2}}{{(t^{6} + 8)}^{2}} d t .$