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IntegrationQuestion and Answers: Page 154

Question Number 105239 Answers: 1 Comments: 0

Σ_(Σ_(p=5) ^6 p) ^(Σ_(p=8) ^(11) p) ∫_(11) ^(13) (((12ky)/x^2 ) + 6x) dx = Σ_(Σ_(p=4) ^7 p) ^(Σ_(p=9) ^(12) p) ∫_(11) ^(16) (x^2 y−(3/2)k)dx solve for y

$\underset{\underset{p = 5}{\sum^{6}} p}{\sum^{\underset{p = 8}{\sum^{11}} p}} \underset{11}{\int^{13}} (\frac{12 k y}{x^{2}} + 6 x) d x = \underset{\underset{p = 4}{\sum^{7}} p}{\sum^{\underset{p = 9}{\sum^{12}} p}} \underset{11}{\int^{16}} (x^{2} y - \frac{3}{2} k) d x$ $s o l v e f o r y$

Question Number 101378 Answers: 2 Comments: 1

∫_(1/e) ^(tanx) (t/(1+t^2 ))dt + ∫_(1/e) ^(cotx) (1/(t(1+t^2 )))dt

$\int_{\frac{1}{e}}^{t a n x} \frac{t}{1 + t^{2}} d t + \int_{\frac{1}{e}}^{c o t x} \frac{1}{t (1 + t^{2})} d t$

Question Number 101373 Answers: 0 Comments: 1

lim_(n→∞ ) Σ_(r=1) ^(4n) ((√n)/((√r)(3(√r)+4(√n))^2 ))

$\lim_{n \to \infty} \underset{r = 1}{\sum^{4 n}} \frac{\sqrt{n}}{\sqrt{r} {(3 \sqrt{r} + 4 \sqrt{n})}^{2}}$

Question Number 101345 Answers: 0 Comments: 3

(1)∫ ((sec^4 x tan x)/(sec^4 x+4)) dx= (2) ∫x^(2x) (2lnx +2) dx = (3) ∫_0 ^1 (√(1−x^2 )) dx =

$(1) \int \frac{\sec^{4} x \tan x}{\sec^{4} x + 4} d x =$ $(2) \int x^{2 x} (2 \ln x + 2) d x =$ $(3) \underset{0}{\int^{1}} \sqrt{1 - x^{2}} d x =$

Question Number 101328 Answers: 0 Comments: 1

this i a beautifull old question in the forum by sir.Ali Esam i Reposted it trying to find any idea to solve I=∫_(−1) ^1 (((sin(x))/(sinh^(−1) (x))))(((sin^(−1) (x))/(sinh(x))))dx i solved it numerical the value is 2.03383

$t h i s i a b e a u t i f u l l o l d q u e s t i o n i n t h e f o r u m$ $b y s i r . A l i E s a m i R e p o s t e d i t t r y i n g t o$ $f i n d a n y i d e a t o s o l v e$ $I = \int_{- 1}^{1} (\frac{s i n (x)}{{s i n h}^{- 1} (x)}) (\frac{{s i n}^{- 1} (x)}{s i n h (x)}) d x$ $i s o l v e d i t n u m e r i c a l$ $t h e v a l u e i s 2.03383$

Question Number 101272 Answers: 1 Comments: 2

∫(√(sec x)) dx

$\int \sqrt{\sec x} d x$

Question Number 101271 Answers: 0 Comments: 2

find ∫ ((xdx)/((√(x^2 +x+1))+(√(x^2 −x+1))))

$find \int \frac{xdx}{\sqrt{x^{2} + x + 1} + \sqrt{x^{2} - x + 1}}$

Question Number 101270 Answers: 0 Comments: 0

calculate ∫_1 ^(+∞) (dx/(x^2 (x+1)^2 (x+2)^2 (x+3)^2 ))

$calculate \int_{1}^{+ \infty} \frac{dx}{x^{2} {(x + 1)}^{2} {(x + 2)}^{2} {(x + 3)}^{2}}$

Question Number 101269 Answers: 1 Comments: 0

calculate ∫_4 ^(+∞) (dx/((x−2)^5 (x+3)^7 ))

$calculate \int_{4}^{+ \infty} \frac{dx}{{(x - 2)}^{5} {(x + 3)}^{7}}$

Question Number 101268 Answers: 1 Comments: 0

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

$calculate \int_{- \infty}^{\infty} \frac{\cos (\arctan (2 x + 1))}{x^{2} + 2 x + 2} dx$

Question Number 101266 Answers: 0 Comments: 0

calculate ∫_1 ^(+∞) (dx/(x^2 (x+1)^3 (x+2)^4 ))

$calculate \int_{1}^{+ \infty} \frac{dx}{x^{2} {(x + 1)}^{3} {(x + 2)}^{4}}$

Question Number 101286 Answers: 0 Comments: 3

∫(((x^m −x^n )^2 )/(√x))dx=?

$\int \frac{{(x^{m} - x^{n})}^{2}}{\sqrt{x}} dx = ?$

Question Number 101234 Answers: 0 Comments: 0

Show that the greatest integer function is Riemann integrable within all segments of R

$S how that the greatest integer function is Riemann$ $integrable within all segments of R$

Question Number 101220 Answers: 1 Comments: 0

∫∫_D (√(x^2 +y^2 ))dxdy D= { (((x,y)∈R, x^2 +y^2 ≥2y, x^2 +y^2 ≤1)),((x≥0 , y≥0)) :}

$\int \int_{D} \sqrt{x^{2} + y^{2}} dxdy D = {\begin{cases} (x, y) \in R, x^{2} + y^{2} ⩾ 2 y, x^{2} + y^{2} ⩽ 1 \\ x ⩾ 0, y ⩾ 0 \end{cases}$

Question Number 101285 Answers: 0 Comments: 1

∫(((x^m −x^n ))/(√x))dx=?

$\int \frac{(x^{m} - x^{n})}{\sqrt{x}} dx = ?$

Question Number 101277 Answers: 2 Comments: 0

∫_0 ^1 (((x−1) dx )/((x+1)ln (x)))

$\underset{0}{\int^{1}} \frac{(x - 1) d x}{(x + 1) \ln (x)}$

Question Number 101192 Answers: 1 Comments: 2

∫ (x/(1+sin x)) dx

$\int \frac{x}{1 + \sin x} d x$

Question Number 101178 Answers: 2 Comments: 0

∫ ((((√x)−x)^2 )/x^2 ) dx ?

$\int \frac{{(\sqrt{x} - x)}^{2}}{x^{2}} dx ?$

Question Number 101073 Answers: 1 Comments: 0

∫_0 ^∞ ((sin(logx))/(logx))dx

$\int_{0}^{\infty} \frac{s i n (l o g x)}{l o g x} d x$

Question Number 101057 Answers: 1 Comments: 0

Find the area bounded the curves f(x)= ∣x^3 −4x^2 +3x∣ and x−axis

$Find the area bounded the$ $curves f (x) = ∣ x^{3} - 4 x^{2} + 3 x ∣ and$ $x - axis$

Question Number 101079 Answers: 2 Comments: 2

Question Number 101023 Answers: 0 Comments: 0

∫tan^(1/5) x cotx secxdx

$\int {t a n}^{\frac{1}{5}} x c o t x s e c x d x$

Question Number 101014 Answers: 0 Comments: 0

Show that ∫_(−∞) ^(+∞) (dx/(1+(x+tanx)^2 )) = π

$S h o w t h a t$ $\int_{- \infty}^{+ \infty} \frac{d x}{1 + {(x + t a n x)}^{2}} = π$

Question Number 101011 Answers: 0 Comments: 5

∫_0 ^∞ ((sinx)/x)dx

$\int_{0}^{\infty} \frac{s i n x}{x} d x$

Question Number 101018 Answers: 0 Comments: 0

∫_(−∞) ^∞ ((log(sin^2 x))/(1+x+e^x ))dx

$\int_{- \infty}^{\infty} \frac{l o g ({s i n}^{2} x)}{1 + x + e^{x}} d x$

Question Number 100969 Answers: 1 Comments: 0

find ∫_(−∞) ^∞ ((sin(cosx))/((x^2 −x+1)^2 ))dx

$find \int_{- \infty}^{\infty} \frac{\sin (cosx)}{{(x^{2} - x + 1)}^{2}} dx$

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