Question and Answers Forum

All Questions Topic List

IntegrationQuestion and Answers: Page 98

Question Number 133038 Answers: 1 Comments: 1

∫_0 ^1 ((x^4 (1−x)^4 )/(1+x^2 )) dx =?

$\underset{0}{\int^{1}} \frac{x^{4} {(1 - x)}^{4}}{1 + x^{2}} d x = ?$

Question Number 133036 Answers: 2 Comments: 0

∫^( (π/2)) _0 (dx/(1+tan^(2014) (x))) = ((πe^q )/p) Find 2p−q.

${\int_{0}}^{\frac{π}{2}} \frac{d x}{1 + \tan^{2014} (x)} = \frac{π e^{q}}{p}$ $Find 2 p - q .$

Question Number 133027 Answers: 4 Comments: 0

∫_0 ^2 x^5 (8−x^3 )^(1/3) dx

${\int^{2}}_{0} x^{5} {(8 - x^{3})}^{\frac{1}{3}} d x$

Question Number 133016 Answers: 3 Comments: 0

∫_0 ^(π/2) (tan(x))^(1/n) dx ...

$\int_{0}^{\frac{π}{2}} {(t a n (x))}^{\frac{1}{n}} d x . . .$

Question Number 133004 Answers: 1 Comments: 0

If ∫ ((tan x)/(1+tan x+tan^2 x)) dx = x−(k/( (√A))) tan^(−1) (((k tan x+1)/( (√A))))+C where C is constant of integration. then the ordered pair (k,A) is equal to

$If \int \frac{\tan x}{1 + \tan x + \tan^{2} x} dx = x - \frac{k}{\sqrt{A}} \tan^{- 1} (\frac{k \tan x + 1}{\sqrt{A}}) + C$ $where C is constant of integration .$ $then the ordered pair (k, A) is$ $equal to$

Question Number 133001 Answers: 0 Comments: 1

Question Number 132987 Answers: 2 Comments: 0

....mathematical analysis... prove that:: 𝛗=∫_0 ^( ∞) ((sin^3 (x))/x^3 )dx=((3π)/8) ∗∗∗∗..........

$. . . . m a t h e m a t i c a l a n a l y s i s . . .$ $p r o v e t h a t :: ϕ = \int_{0}^{\infty} \frac{{s i n}^{3} (x)}{x^{3}} d x = \frac{3 π}{8}$ $* * * * . . . . . . . . . .$

Question Number 132927 Answers: 0 Comments: 0

Question Number 132925 Answers: 1 Comments: 0

(∫_0 ^(π/2) (√(sin(x)))dx)^2 +(∫_0 ^(π/2) (√(cos(x)))dx)^2 <8((√2)−1)

${(\int_{0}^{\frac{π}{2}} \sqrt{s i n (x)} d x)}^{2} + {(\int_{0}^{\frac{π}{2}} \sqrt{c o s (x)} d x)}^{2} < 8 (\sqrt{2} - 1)$

Question Number 132901 Answers: 2 Comments: 0

∫_(−π/2) ^(3π/2) (sin^(−1) (∣sin x∣)+cos^(−1) (∣cos x∣)) dx

$\int_{- π / 2}^{3 π / 2} (\sin^{- 1} (∣ \sin x ∣) + \cos^{- 1} (∣ \cos x ∣)) dx$

Question Number 132877 Answers: 1 Comments: 0

.... nice calculus... prove that : 𝛗=∫_0 ^( ∞) ((sin(x).log^2 (x))/x) =(π/(24))(12γ^( 2) +π^2 ) .....

$. . . . n i c e c a l c u l u s . . .$ $p r o v e t h a t :$ $ϕ = \int_{0}^{\infty} \frac{s i n (x) . {l o g}^{2} (x)}{x}$ $= \frac{π}{24} (12 γ^{2} + π^{2}) . . . . .$

Question Number 132876 Answers: 0 Comments: 1

Question Number 132852 Answers: 0 Comments: 0

∫(x−1)^(x+1) dx

$\int {(x - 1)}^{x + 1} d x$

Question Number 132838 Answers: 1 Comments: 0

Question Number 132798 Answers: 2 Comments: 0

∫_0 ^(π/2) ((√(sin (x)))+(√(cos (x))))dx

${\int^{\frac{π}{2}}}_{0} (\sqrt{\sin (x)} + \sqrt{\cos (x)}) d x$

Question Number 132765 Answers: 2 Comments: 0

Question Number 132755 Answers: 3 Comments: 1

Question Number 132733 Answers: 1 Comments: 0

∫_0 ^∞ ((log x)/(1+x^2 +x^4 )) dx=...?

$\int_{0}^{\infty} \frac{\log x}{1 + x^{2} + x^{4}} d x = . . . ?$

Question Number 132729 Answers: 3 Comments: 0

....advanced calculus... evaluate : 𝛗=∫_0 ^( ∞) xe^(−2x) ln(x)dx=???

$. . . . a d v a n c e d c a l c u l u s . . .$ $e v a l u a t e :$ $ϕ = \int_{0}^{\infty} {x e}^{- 2 x} l n (x) d x = ? ? ?$

Question Number 132708 Answers: 2 Comments: 0

∫_(−∞) ^∞ ((x^2 cos (px+q))/(x^2 +(p+q)^2 ))dx

$\int_{- \infty}^{\infty} \frac{x^{2} \cos (p x + q)}{x^{2} + {(p + q)}^{2}} d x$

Question Number 132693 Answers: 2 Comments: 0

I=∫ (dx/(x(x^2 +1)^3 ))

$I = \int \frac{d x}{x {(x^{2} + 1)}^{3}}$

Question Number 132610 Answers: 2 Comments: 0

Ω=∫ ((sin^2 (x))/(1+sin^2 (x))) dx

$Ω = \int \frac{\sin^{2} (x)}{1 + \sin^{2} (x)} dx$

Question Number 132600 Answers: 0 Comments: 0

Question Number 132598 Answers: 0 Comments: 0

Find the voloume bounded by z=(√(x^2 +y^2 )) and the plane y+z=3

$Find the voloume bounded by z = \sqrt{x^{2} + y^{2}}$ $and the plane y + z = 3$

Question Number 132534 Answers: 3 Comments: 1

∫_0 ^(π/2) (dx/(1+sin x)) →diverges or converges?

$\int_{0}^{\frac{π}{2}} \frac{dx}{1 + \sin x} \to diverges or converges ?$

Question Number 132519 Answers: 1 Comments: 0

.... nice calculus.... prove that :: Σ_(n=1) ^∞ (((−1)^n ln(n))/n)=γln(2)−(1/2)ln^2 (2)

$. . . . n i c e c a l c u l u s . . . .$ $p r o v e t h a t ::$ $\underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n} l n (n)}{n} = γ l n (2) - \frac{1}{2} {l n}^{2} (2)$

Pg 93 Pg 94 Pg 95 Pg 96 Pg 97 Pg 98 Pg 99 Pg 100 Pg 101 Pg 102

Contact: info@tinkutara.com