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IntegrationQuestion and Answers: Page 221

Question Number 65485 Answers: 2 Comments: 0

∫e^(cos^(−1) (x)) dx

$\int e^{{c o s}^{- 1} (x)} d x$

Question Number 65478 Answers: 0 Comments: 1

Question Number 65455 Answers: 0 Comments: 2

find U_n = ∫_0 ^(+∞) (((−1)^x )/(2^x^2 (x^2 +4n^2 )))dx (n from N and n≥1) study nature of the serie Σ 2^n^2 U_n

$f i n d U_{n} = \int_{0}^{+ \infty} \frac{{(- 1)}^{x}}{2^{x^{2}} (x^{2} + 4 n^{2})} d x (n f r o m N a n d n ⩾ 1)$ $s t u d y n a t u r e o f t h e s e r i e Σ 2^{n^{2}} U_{n}$

Question Number 65450 Answers: 0 Comments: 1

Question Number 65445 Answers: 0 Comments: 2

find f(x) =∫_0 ^(π/4) ln(cost +xsint)dt

$f i n d f (x) = \int_{0}^{\frac{π}{4}} l n (c o s t + x s i n t) d t$

Question Number 65443 Answers: 0 Comments: 0

Question Number 65420 Answers: 0 Comments: 0

Question Number 65401 Answers: 0 Comments: 1

let f(x,y)=(x+y)(√(x+y−1)) calculate ∫∫_D f(x,y)dxdy with D ={(x,y)∈R^2 / 1≤x≤2 and 1≤y≤(√3)}

$l e t f (x, y) = (x + y) \sqrt{x + y - 1}$ $c a l c u l a t e \int \int_{D} f (x, y) d x d y w i t h$ $D = {(x, y) \in R^{2} / 1 ⩽ x ⩽ 2 a n d 1 ⩽ y ⩽ \sqrt{3}}$

Question Number 65400 Answers: 0 Comments: 0

find f(α) =∫_1 ^(+∞) ((arctan((α/x)))/(1+x^2 )) dx with α≥0

$f i n d f (α) = \int_{1}^{+ \infty} \frac{a r c t a n (\frac{α}{x})}{1 + x^{2}} d x w i t h α ⩾ 0$

Question Number 65398 Answers: 0 Comments: 1

1) calculate A_n =∫∫_([1,n[^2 ) sin(x^2 +3y^2 ) e^(−x^2 −3y^2 ) dxdy 2) determine lim_(n→+∞) A_n

$1) c a l c u l a t e A_{n} = \int \int_{[1, n [^{2}} s i n (x^{2} + 3 y^{2}) e^{- x^{2} - 3 y^{2}} d x d y$ $2) d e t e r m i n e {l i m}_{n \to + \infty} A_{n}$

Question Number 65399 Answers: 0 Comments: 1

1) calculate A_n = ∫∫_([0,n[^2 ) ((dxdy)/(√(x^2 +y^2 +4))) 2)find lim_(n→+∞) A_n

$1) c a l c u l a t e A_{n} = \int \int_{[0, n [^{2}} \frac{d x d y}{\sqrt{x^{2} + y^{2} + 4}}$ $2) f i n d {l i m}_{n \to + \infty} A_{n}$

Question Number 65395 Answers: 1 Comments: 1

Question Number 65387 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(2x)−arctanx)/x)dx

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

Question Number 65372 Answers: 0 Comments: 4

I=∫_1 ^e (dx/(x(1+ln^2 x)))

$I = \int_{1}^{e} \frac{d x}{x (1 + {l n}^{2} x)}$

Question Number 65355 Answers: 2 Comments: 1

find ∫ (dx/(√((x+1)(x+2)(x+3))))

$f i n d \int \frac{d x}{\sqrt{(x + 1) (x + 2) (x + 3)}}$

Question Number 65354 Answers: 0 Comments: 3

find ∫ (dx/(√(x^2 +x−2)))

$f i n d \int \frac{d x}{\sqrt{x^{2} + x - 2}}$

Question Number 65352 Answers: 0 Comments: 1

give the integralA_n = ∫_1 ^(+∞) (dt/(1+x^n )) with n integr and n≥2 at form of serie.

$g i v e t h e {i n t e g r a l A}_{n} = \int_{1}^{+ \infty} \frac{d t}{1 + x^{n}} w i t h n i n t e g r a n d n ⩾ 2$ $a t f o r m o f s e r i e .$

Question Number 65332 Answers: 0 Comments: 1

Question Number 65307 Answers: 1 Comments: 0

∫(((4x+3)dx)/(√(2x^2 +2x−3))) = ?

$\int \frac{(4 x + 3) d x}{\sqrt{2 x^{2} + 2 x - 3}} = ?$

Question Number 65321 Answers: 0 Comments: 0

Question Number 65320 Answers: 0 Comments: 1

Question Number 65319 Answers: 3 Comments: 2

Question Number 65293 Answers: 0 Comments: 3

1) calculate ∫_(−∞) ^(+∞) (dx/(x−a)) with a ∈C 2) find the values of ∫_0 ^∞ (dx/(x^4 +1)) and ∫_0 ^∞ (dx/(x^6 +1)) by using the decomposition inside C(x).

$1) c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{d x}{x - a} w i t h a \in C$ $2) f i n d t h e v a l u e s o f \int_{0}^{\infty} \frac{d x}{x^{4} + 1} a n d \int_{0}^{\infty} \frac{d x}{x^{6} + 1}$ $b y u s i n g t h e d e c o m p o s i t i o n i n s i d e C (x) .$

Question Number 65290 Answers: 1 Comments: 3

f(x) =∫_0 ^1 (dt/(x+e^t )) with 0≤x≤1 1) find aexplicit form of f(x) 2) calculate ∫_0 ^1 (dt/(2+e^t )) 3) find g(x) =∫_0 ^1 (dt/((x+e^t )^2 )) 4) calculate ∫_0 ^1 (dt/((1+e^t )^2 )) 5) give f^((n)) (x) at form of integrals 6) developp f at integr serie.

$f (x) = \int_{0}^{1} \frac{d t}{x + e^{t}} w i t h 0 ⩽ x ⩽ 1$ $1) f i n d a e x p l i c i t f o r m o f f (x)$ $2) c a l c u l a t e \int_{0}^{1} \frac{d t}{2 + e^{t}}$ $3) f i n d g (x) = \int_{0}^{1} \frac{d t}{{(x + e^{t})}^{2}}$ $4) c a l c u l a t e \int_{0}^{1} \frac{d t}{{(1 + e^{t})}^{2}}$ $5) g i v e f^{(n)} (x) a t f o r m o f i n t e g r a l s$ $6) d e v e l o p p f a t i n t e g r s e r i e .$

Question Number 65288 Answers: 0 Comments: 4

1) let f(x) =∫_0 ^(+∞) (dt/(t^3 +x^3 )) with x>0 calculate f(x) 2) find also g(x) =∫_0 ^∞ (dt/((t^3 +x^3 )^2 )) 3) find the values of integrals ∫_0 ^∞ (dt/(t^3 +1)) and ∫_0 ^∞ (dt/((t^3 +1)^2 )) 4) give f^((n)) (x) at form of integrals.

$1) l e t f (x) = \int_{0}^{+ \infty} \frac{d t}{t^{3} + x^{3}} w i t h x > 0$ $c a l c u l a t e f (x)$ $2) f i n d a l s o g (x) = \int_{0}^{\infty} \frac{d t}{{(t^{3} + x^{3})}^{2}}$ $3) f i n d t h e v a l u e s o f i n t e g r a l s \int_{0}^{\infty} \frac{d t}{t^{3} + 1} a n d \int_{0}^{\infty} \frac{d t}{{(t^{3} + 1)}^{2}}$ $4) g i v e f^{(n)} (x) a t f o r m o f i n t e g r a l s .$

Question Number 65287 Answers: 0 Comments: 1

let f(x) =x∣x∣ 2π periodic odd developp f at fourier series

$l e t f (x) = x ∣ x ∣ 2 π p e r i o d i c o d d$ $d e v e l o p p f a t f o u r i e r s e r i e s$

Pg 216 Pg 217 Pg 218 Pg 219 Pg 220 Pg 221 Pg 222 Pg 223 Pg 224 Pg 225

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