Question and Answers Forum

IntegrationQuestion and Answers: Page 39

Question Number 170501 Answers: 1 Comments: 0

solve this: ∫∫_D x^2 e^(xy) dxdy D:{(x.y)∈R^2 /0≤x≤1. 0≤y≤2} ∫∫_D ((ydxdy)/((1+x^2 +y^2 )^(3/2) )). 0≤x≤1.0≤y≤1.

$s o l v e t h i s :$ $\int \int_{D} x^{2} e^{x y} d x d y$ $D : {(x . y) \in R^{2} / 0 ⩽ x ⩽ 1 . 0 ⩽ y ⩽ 2}$ $\int \int_{D} \frac{y d x d y}{{(1 + x^{2} + y^{2})}^{\frac{3}{2}}} . 0 ⩽ x ⩽ 1.0 ⩽ y ⩽ 1 .$

Question Number 170475 Answers: 0 Comments: 0

An easy question of Measure theory: Prove that : μ ( Q )=0 ■m.n

$A n e a s y q u e s t i o n o f M e a s u r e t h e o r y :$ $P r o v e t h a t : μ (Q) = 0 ◼ m . n$

Question Number 170388 Answers: 0 Comments: 0

Question Number 170384 Answers: 0 Comments: 0

Prove that ∫_0 ^( (π/2)) ln(a−sin^2 (x))dx=πln((√((a−1)/a))+1)+(π/2)ln((a/4)) a>0 Im{a}≠0

$Prove that$ $\int_{0}^{\frac{π}{2}} \ln (a - \sin^{2} (x)) dx = π \ln (\sqrt{\frac{a - 1}{a}} + 1) + \frac{π}{2} \ln (\frac{a}{4})$ $a > 0 I m {a} \neq 0$

Question Number 170368 Answers: 0 Comments: 0

Question Number 170349 Answers: 1 Comments: 0

help please ∫_1 ^∞ ((1/t)−sin^(−1) ((1/t))) dt I can show that it is equal to −Σ_(n≥0) (−1)^n (((2n−1)!)/(4^n (n!)^2 (2n+1))) but I cant calculate it...

$h e l p p l e a s e$ ${\int^{\infty}}_{1} (\frac{1}{t} - \sin^{- 1} (\frac{1}{t})) d t$ $I c a n s h o w t h a t i t i s e q u a l t o$ $- \sum_{n ⩾ 0} {(- 1)}^{n} \frac{(2 n - 1)!}{4^{n} {(n!)}^{2} (2 n + 1)}$ $b u t I c a n t c a l c u l a t e i t . . .$

Question Number 170189 Answers: 0 Comments: 2

Question Number 170255 Answers: 1 Comments: 0

(d/dx)[∫_2 ^x e^t^2 dt=?

$\frac{d}{d x} [\int_{2}^{x} e^{t^{2}} d t = ?$

Question Number 170109 Answers: 0 Comments: 0

Question Number 169930 Answers: 0 Comments: 0

find f(α)=∫_0 ^1 ((arctan(αx))/(1+x^2 ))dx

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

Question Number 169906 Answers: 0 Comments: 0

Evaluate ∫∫e^(2x+3y) dxdy over the triangle bounded by the lines x = 0, y = 0, x+y = 1.

$Evaluate \int \int e^{2 x + 3 y} d x d y over the triangle$ $bounded by the lines x = 0, y = 0, x + y = 1 .$

Question Number 169873 Answers: 2 Comments: 0

∫_0 ^1 ((ln(1+x))/x)dx=?

$\underset{0}{\int^{1}} \frac{l n (1 + x)}{x} d x = ?$

Question Number 169864 Answers: 1 Comments: 0

Question Number 169825 Answers: 1 Comments: 0

Question Number 169706 Answers: 0 Comments: 0

using cylindrical coordinates { ((x=rcosθ)),((y = rsin θ)),((z=z)) :} to evaluate the integral K= ∫∫∫_S (√(x^2 +y^2 −z^2 )) dxdydz where S= {(x,y,z) ∈R^3 : x^2 +y^2 ≤ 4, 0 ≤z≤(√(x^2 +y^2 ))}

$using cylindrical coordinates {\begin{cases} x = r \cos θ \\ y = r \sin θ \\ z = z \end{cases}$ $to evaluate the integral$ $K = \int \int \int_{S} \sqrt{x^{2} + y^{2} - z^{2}} d x d y d z$ $where$ $S = {(x, y, z) \in R^{3} : x^{2} + y^{2} ⩽ 4, 0 ⩽ z ⩽ \sqrt{x^{2} + y^{2}}}$