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IntegrationQuestion and Answers: Page 216

Question Number 66693 Answers: 1 Comments: 1

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

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

Question Number 66627 Answers: 1 Comments: 4

Question Number 66589 Answers: 2 Comments: 5

∫((sinx)/(1+sinx+sin2x))dx

$\int \frac{s i n x}{1 + s i n x + s i n 2 x} d x$

Question Number 66564 Answers: 0 Comments: 0

Question Number 66561 Answers: 1 Comments: 2

evaluate ∫_0 ^2 ∣ x+ 2∣ dx.

$e v a l u a t e$ $\int_{0}^{2} ∣ x + 2 ∣ d x .$

Question Number 66550 Answers: 0 Comments: 2

∫_0 ^1 ∫_((y/2) ) ^((1/2) ) e^(−x^2 ) dxdy=?

$\int_{0}^{1} \int_{\frac{y}{2}}^{\frac{1}{2}} e^{- x^{2}} d x d y = ?$

Question Number 66540 Answers: 0 Comments: 0

graph the function r^2 =cos(2θ) and find the area?

$g r a p h t h e f u n c t i o n r^{2} = c o s (2 θ) a n d f i n d t h e a r e a ?$

Question Number 66536 Answers: 0 Comments: 0

∫ln^(10) (x) sin^7 (x) dx

$\int {l n}^{10} (x) {s i n}^{7} (x) d x$

Question Number 66520 Answers: 0 Comments: 1

find the length r=2/1−cosθ if θ between pi/2 to pi

$f i n d t h e l e n g t h r = 2 / 1 - c o s θ i f θ b e t w e e n p i / 2 t o p i$

Question Number 66517 Answers: 1 Comments: 1

find the area cos(2θ)

$f i n d t h e a r e a c o s (2 θ)$

Question Number 66502 Answers: 1 Comments: 0

find the area about cos(2θ)

$f i n d t h e a r e a a b o u t c o s (2 θ)$

Question Number 66483 Answers: 0 Comments: 4

calculate Σ_(k=2) ^∞ (((−1)^k )/k) ζ(k) if ζ(s)=Σ_(n=1) ^∞ (1/n^s )

$c a l c u l a t e \underset{k = 2}{\sum^{\infty}} \frac{{(- 1)}^{k}}{k} ζ (k) i f ζ (s) = \underset{n = 1}{\sum^{\infty}} \frac{1}{n^{s}}$

Question Number 66476 Answers: 0 Comments: 1

Question Number 66474 Answers: 0 Comments: 2

∫e^x^2 dx=?

$\int e^{x^{2}} d x = ?$

Question Number 66470 Answers: 0 Comments: 5

calculate ∫_0 ^∞ (dx/((x^n +8)^3 )) withn>1

$c a l c u l a t e \int_{0}^{\infty} \frac{d x}{{(x^{n} + 8)}^{3}} w i t h n > 1$

Question Number 66468 Answers: 0 Comments: 1

calculate I_n = ∫_0 ^∞ (dx/((x^n +3)^2 )) with n>1

$c a l c u l a t e I_{n} = \int_{0}^{\infty} \frac{d x}{{(x^{n} + 3)}^{2}} w i t h n > 1$

Question Number 66466 Answers: 0 Comments: 1

find f(a,b) =∫_0 ^∞ ((cos(ax)cos(bx))/((x^2 +a^2 )(x^2 +b^2 )))dx with a>0 and b>0 2)calculate ∫_0 ^∞ ((cos(x)cos(2x))/((x^2 +1)(x^2 +4)))dx

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

Question Number 66465 Answers: 0 Comments: 1

calculate ∫_0 ^∞ (dx/((x^2 +2i)( x^2 +4j))) with i=e^((iπ)/2) and j=e^(i((2π)/3))

$c a l c u l a t e \int_{0}^{\infty} \frac{d x}{(x^{2} + 2 i) (x^{2} + 4 j)} w i t h i = e^{\frac{i π}{2}} a n d j = e^{i \frac{2 π}{3}}$

Question Number 66464 Answers: 0 Comments: 1

calculate ∫_0 ^∞ (dx/((x^2 +3)(x^2 +8)^2 ))

$c a l c u l a t e \int_{0}^{\infty} \frac{d x}{(x^{2} + 3) {(x^{2} + 8)}^{2}}$

Question Number 66459 Answers: 0 Comments: 1

1) calculate by residus method ∫_0 ^∞ (dx/((1+x^2 )^3 )) 2) find the value of ∫_0 ^1 ((1+x^4 )/((1+x^2 )^3 ))dx

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

Question Number 66446 Answers: 0 Comments: 1

Find ∫_1 ^∞ ((1/(E(x))) −(1/x))dx

$F i n d \int_{1}^{\infty} (\frac{1}{E (x)} - \frac{1}{x}) d x$

Question Number 66405 Answers: 0 Comments: 0

Question Number 66404 Answers: 0 Comments: 3

Question Number 66403 Answers: 0 Comments: 0

Question Number 66401 Answers: 0 Comments: 0

Question Number 66351 Answers: 0 Comments: 1

let I_n =∫_0 ^∞ (e^(nt) /((1+e^t )^(n+1) ))dt (n from N^★ ) )prove the existence of I_n 2)find lim_(n→+∞) I_n

$l e t I_{n} = \int_{0}^{\infty} \frac{e^{n t}}{{(1 + e^{t})}^{n + 1}} d t (n f r o m N^{★})$ $) p r o v e t h e e x i s t e n c e o f I_{n}$ $2) f i n d {l i m}_{n \to + \infty} I_{n}$

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