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IntegrationQuestion and Answers: Page 197

Question Number 78305 Answers: 0 Comments: 0

∫^∞^ 5646778727711=778888877−{116567×622−[66262−712]66666}

$\int^{\hat{\infty}} 5646778727711 = 778888877 - {116567 \times 622 - [66262 - 712] 66666}$

Question Number 78284 Answers: 0 Comments: 1

calculate ∫∫_D xy(√(x^2 +2y^2 ))dxdy D={(x,y)/0≤x≤1 and 0≤y≤(√(1−x^2 ))}

$c a l c u l a t e \int \int_{D} x y \sqrt{x^{2} + 2 y^{2}} d x d y$ $D = {(x, y) / 0 ⩽ x ⩽ 1 a n d 0 ⩽ y ⩽ \sqrt{1 - x^{2}}}$

Question Number 78283 Answers: 0 Comments: 3

calculate ∫∫_D (x^2 +2y)dxdy with D={(x,y)∈R^2 / x^2 ≥y and y≥x^2 }

$c a l c u l a t e \int \int_{D} (x^{2} + 2 y) d x d y$ $w i t h D = {(x, y) \in R^{2} / x^{2} ⩾ y a n d y ⩾ x^{2}}$

Question Number 78281 Answers: 0 Comments: 0

calculate ∫∫_W ((x^2 −3y^2 )/e^(x^2 +y^2 ) )dxdy with W =[0,1]×[0,1]

$c a l c u l a t e \int \int_{W} \frac{x^{2} - 3 y^{2}}{e^{x^{2} + y^{2}}} d x d y$ $w i t h W = [0, 1] \times [0, 1]$

Question Number 78277 Answers: 0 Comments: 0

calculate ∫∫_W (e^(−x^2 −y^2 ) /(2(√(x^2 +y^2 ))+3))dxdy with W ={ (x,y)/ x>0 and y>0}

$c a l c u l a t e \int \int_{W} \frac{e^{- x^{2} - y^{2}}}{2 \sqrt{x^{2} + y^{2}} + 3} d x d y$ $w i t h W = {(x, y) / x > 0 a n d y > 0}$

Question Number 78276 Answers: 0 Comments: 1

find I_n =∫∫_([1,n]^2 ) (√(x^2 +y^2 ))ln(x^2 +y^2 )dxdy

$f i n d I_{n} = \int \int_{{[1, n]}^{2}} \sqrt{x^{2} + y^{2}} l n (x^{2} + y^{2}) d x d y$

Question Number 78273 Answers: 0 Comments: 1

let f(θ) =∫_0 ^(π/4) (dx/(1+sinθ sinx)) with 0<θ<(π/2) 1) explicite f(θ) 2) calculate ∫_0 ^(π/4) (dx/((1+sinθ sinx)^2 ))

$l e t f (θ) = \int_{0}^{\frac{π}{4}} \frac{d x}{1 + s i n θ s i n x}$ $w i t h 0 < θ < \frac{π}{2}$ $1) e x p l i c i t e f (θ)$ $2) c a l c u l a t e \int_{0}^{\frac{π}{4}} \frac{d x}{{(1 + s i n θ s i n x)}^{2}}$

Question Number 78271 Answers: 0 Comments: 1

calculate A_θ =∫_0 ^(π/2) (dx/(2+cosθ sinx)) −π<θ<π

$c a l c u l a t e A_{θ} = \int_{0}^{\frac{π}{2}} \frac{d x}{2 + c o s θ s i n x}$ $- π < θ < π$

Question Number 78270 Answers: 1 Comments: 1

find ∫_0 ^1 ((ln(1−x^2 )ln(x))/x^2 )dx prove first the convergence.

$f i n d \int_{0}^{1} \frac{l n (1 - x^{2}) l n (x)}{x^{2}} d x$ $p r o v e f i r s t t h e c o n v e r g e n c e .$

Question Number 78269 Answers: 1 Comments: 1

let f(a) =∫_0 ^∞ ((cos(ax))/(x^2 +a^2 ))dx with a>0 find ∫_1 ^2 f(a)da

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

Question Number 78267 Answers: 0 Comments: 1

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

$f i n d \int_{- \infty}^{+ \infty} \frac{x^{2} - x}{x^{4} - x^{2} + 3} d x$

Question Number 78266 Answers: 1 Comments: 2

calculate f(a)=∫_0 ^1 ln(1−ax^3 )dx with 0<a<1

$c a l c u l a t e f (a) = \int_{0}^{1} l n (1 - {a x}^{3}) d x$ $w i t h 0 < a < 1$

Question Number 78264 Answers: 0 Comments: 4

let I =∫_0 ^π x cos^4 x dxand J=∫_0 ^π x sin^4 xdx 1) calculate I+J and I−J 2) find the values of I and J

$l e t I = \int_{0}^{π} x {c o s}^{4} x d x a n d J = \int_{0}^{π} x {s i n}^{4} x d x$ $1) c a l c u l a t e I + J a n d I - J$ $2) f i n d t h e v a l u e s o f I a n d J$

Question Number 78265 Answers: 1 Comments: 0

find ∫ ((sin^3 x)/(tan^5 x))dx

$f i n d \int \frac{{s i n}^{3} x}{{t a n}^{5} x} d x$

Question Number 78251 Answers: 1 Comments: 0

∫((x+4)/(x−(x)^(1/3) )) dx

$\int \frac{x + 4}{x - \sqrt[3]{x}} d x$

Question Number 78198 Answers: 1 Comments: 4

Question Number 78163 Answers: 0 Comments: 2

∫ (√(1 + 3 sin(θ) + sin^2 (θ))) dθ

$\int \sqrt{1 + 3 \sin (θ) + \sin^{2} (θ)} d θ$

Question Number 78135 Answers: 0 Comments: 0

explicit f(x)=∫_0 ^∞ ((arctan(xt))/(t^2 +x^2 ))dt with x>0

$e x p l i c i t f (x) = \int_{0}^{\infty} \frac{a r c t a n (x t)}{t^{2} + x^{2}} d t$ $w i t h x > 0$

Question Number 78134 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^(+∞) ((arctan(3x^2 ))/(x^2 +4))dx

$f i n d t h e v a l u e o f \int_{- \infty}^{+ \infty} \frac{a r c t a n (3 x^{2})}{x^{2} + 4} d x$

Question Number 78254 Answers: 0 Comments: 0

∫_0 ^1 ((xln(ln((1/x))))/((x^2 −x+1)^2 ))dx i poste solution later!

$\int_{0}^{1} \frac{xln (\ln (\frac{1}{x}))}{{(x^{2} - x + 1)}^{2}} dx$ $i poste solution later!$

Question Number 78013 Answers: 1 Comments: 0

if : 30x^4 −((15)/8)= ∫_t ^x g(u)du find g(t).

$i f : 30 x^{4} - \frac{15}{8} = \underset{t}{\int^{x}} g (u) d u$ $f i n d g (t) .$

Question Number 77995 Answers: 0 Comments: 3

calculate ∫_(−∞) ^(+∞) ((arctan(2x+1))/((x^2 +3)^2 ))dx

$c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{a r c t a n (2 x + 1)}{{(x^{2} + 3)}^{2}} d x$

Question Number 77987 Answers: 0 Comments: 0

Question Number 77962 Answers: 1 Comments: 2

∫(dx/(1+(tan(x))^(√2) )) dx

$\int \frac{d x}{1 + {(t a n (x))}^{\sqrt{2}}} d x$

Question Number 77960 Answers: 0 Comments: 3

∫ ((2x^3 −1)/(x^4 +x)) dx?

$\int \frac{2 x^{3} - 1}{x^{4} + x} d x ?$

Question Number 77918 Answers: 1 Comments: 1

∫ _0 ^π e^(−2x) sin x dx ?

$\int \underset{0}{\overset{π}{}} e^{- 2 x} \sin x d x ?$

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