Question and Answers Forum

IntegrationQuestion and Answers: Page 100

Question Number 131505 Answers: 4 Comments: 1

If ∫_a ^b f(x)dx = ∫_a ^b g(x)dx is f(x)=g(x) ? true or false?

$If \int_{a}^{b} f (x) dx = \int_{a}^{b} g (x) dx$ $is f (x) = g (x) ?$ $true or false ?$

Question Number 131496 Answers: 3 Comments: 0

Given f(x)=f(x+(π/6)) ∀x∈R if ∫_0 ^( (π/6)) f(x)dx= T find the value of ∫_π ^( ((4π)/3)) f(x+π)dx. nice integral

$Given f (x) = f (x + \frac{π}{6}) \forall x \in R$ $if \int_{0}^{\frac{π}{6}} f (x) dx = T find the value$ $of \int_{π}^{\frac{4 π}{3}} f (x + π) dx .$ $nice integral$

Question Number 131405 Answers: 5 Comments: 2

…… super cooles Integral ⋰⋰ ∫_0 ^( ∞) (dx/((1+x^2 )^2 )) =?

$\dots \dots super cooles Integral \iddots \iddots$ $\int_{0}^{\infty} \frac{d x}{{(1 + x^{2})}^{2}} = ?$

Question Number 131401 Answers: 1 Comments: 0

...nice calculus... prove that::: ∫_0 ^( 1) (Arcsin(x)).(Arccos(x))dx=^(??) 2−(π/2)

$. . . n i c e c a l c u l u s . . .$ $p r o v e t h a t :::$ $\int_{0}^{1} (A r c s i n (x)) . (A r c c o s (x)) d x \overset{? ?}{=} 2 - \frac{π}{2}$

Question Number 131364 Answers: 1 Comments: 0

How can I calculate the volume of a region bounded by y=x^2 +3 ;x=1 and x=2 rotating about the y=7 using the shell method.

$How can I calculate the volume$ $of a region bounded by y = x^{2} + 3; x = 1$ $and x = 2 rotating about the y = 7 using$ $the shell method .$

Question Number 131286 Answers: 2 Comments: 0

... calculus .... find :: i:: Σ_(n=2) ^∞ (((−1)^n )/(n^2 −1))=? ii:: Σ_(n=2) ^∞ ((((−1)^n )/(n^4 −1)))=?

$. . . c a l c u l u s . . . .$ $f i n d :: i :: \underset{n = 2}{\sum^{\infty}} \frac{{(- 1)}^{n}}{n^{2} - 1} = ?$ $i i :: \underset{n = 2}{\sum^{\infty}} (\frac{{(- 1)}^{n}}{n^{4} - 1}) = ?$

Question Number 131247 Answers: 8 Comments: 0

(1) ψ = ∫ (dx/(1−sin x cos x))=? (2) ∫_0 ^( ∞) (x/(x^3 +1)) dx =? (3) ∫_0 ^∞ (1/(x^(3/2) +1)) dx =?

$(1) ψ = \int \frac{d x}{1 - \sin x \cos x} = ?$ $(2) \int_{0}^{\infty} \frac{x}{x^{3} + 1} d x = ?$ $(3) \int_{0}^{\infty} \frac{1}{x^{3 / 2} + 1} d x = ?$

Question Number 131245 Answers: 2 Comments: 0

Find ∫_(−b) ^b ∫_(−a) ^a ((dxdy)/( (x^2 +y^2 +h^2 )^(3/2) ))

$Find$ $\int_{- b}^{b} \int_{- a}^{a} \frac{d x d y}{{(x^{2} + y^{2} + h^{2})}^{3 / 2}}$

Question Number 131227 Answers: 1 Comments: 0

... real analysis ... prove:: 𝛀= ∫_0 ^( 1) ln(ln((1/x)))ln^2 (x)dx=3−2γ

$. . . r e a l a n a l y s i s . . .$ $p r o v e ::$ $Ω = \int_{0}^{1} l n (l n (\frac{1}{x})) {l n}^{2} (x) d x = 3 - 2 γ$

Question Number 131211 Answers: 1 Comments: 0

...calculus... prove that:: 𝚽=∫_0 ^( (𝛑/4)) (((√(tan(x)+tan^2 (x)))/( (√(tan(x)−tan^2 (x))))) sin(x))dx =(1/2)+((√𝛑)/8) (((𝚪((1/4)))/(𝚪((3/4))))−((𝚪((3/4)))/(𝚪((5/4)))))

$. . . c a l c u l u s . . .$ $p r o v e t h a t ::$ $Φ = \int_{0}^{\frac{π}{4}} (\frac{\sqrt{t a n (x) + {t a n}^{2} (x)}}{\sqrt{t a n (x) - {t a n}^{2} (x)}} s i n (x)) d x$ $= \frac{1}{2} + \frac{\sqrt{π}}{8} (\frac{Γ (\frac{1}{4})}{Γ (\frac{3}{4})} - \frac{Γ (\frac{3}{4})}{Γ (\frac{5}{4})})$

Question Number 131189 Answers: 0 Comments: 0

∫((−sin(ln(k^x )))/( (√k)))dx=??

$\int \frac{- s i n (l n (k^{x}))}{\sqrt{k}} d x = ? ?$

Question Number 131187 Answers: 0 Comments: 0

Question Number 131183 Answers: 1 Comments: 0

Question Number 131176 Answers: 1 Comments: 0

∫((cos(ln(a^x )))/( (√k)))dx=??

$\int \frac{c o s (l n (a^{x}))}{\sqrt{k}} d x = ? ?$

Question Number 131167 Answers: 2 Comments: 0

Question Number 131147 Answers: 1 Comments: 1

∫_( 0) ^( 1) ((3x^2 −1)/(1+(√(x−x^3 )))) dx =?

$\int_{0}^{1} \frac{3 x^{2} - 1}{1 + \sqrt{x - x^{3}}} d x = ?$

Question Number 131146 Answers: 1 Comments: 1

Given f(x)=f(x+6) ∀x∈R If ∫_(−2) ^( 2) f(x)dx=−2 and ∫_(−2) ^( 4) f(x)dx=2 find the value of ∫_4 ^( 10) f(x)dx.

$G i v e n f (x) = f (x + 6) \forall x \in R$ $I f \int_{- 2}^{2} f (x) d x = - 2 a n d \int_{- 2}^{4} f (x) d x = 2$ $f i n d t h e v a l u e o f \int_{4}^{10} f (x) d x .$

Question Number 131138 Answers: 1 Comments: 0

∫_0 ^( 1) ((arctan (√(x^2 +2)))/((x^2 +1)(√(x^2 +2)))) dx =?

$\int_{0}^{1} \frac{\arctan \sqrt{x^{2} + 2}}{(x^{2} + 1) \sqrt{x^{2} + 2}} dx = ?$

Question Number 131135 Answers: 0 Comments: 1

Question Number 131073 Answers: 1 Comments: 0

Question Number 131068 Answers: 1 Comments: 0

∫ sin^2 x cos 4x dx =?

$\int \sin^{2} x \cos 4 x d x = ?$

Question Number 131058 Answers: 1 Comments: 0

∫(((x^2 +2)(x^2 +3)(x^2 +4))/((x^2 +5)(x^2 +6)(x^2 +7))) dx

$\int \frac{(x^{2} + 2) (x^{2} + 3) (x^{2} + 4)}{(x^{2} + 5) (x^{2} + 6) (x^{2} + 7)} dx$

Question Number 131053 Answers: 1 Comments: 0

∫((x^2 +2)/(x^4 +4))dx

$\int \frac{x^{2} + 2}{x^{4} + 4} dx$

Question Number 131050 Answers: 1 Comments: 0

let f(x)=∫_0 ^∞ ((tsin(xt))/((x^2 +t^2 )^2 ))dt (x>0) calculate f^′ (x)

$let f (x) = \int_{0}^{\infty} \frac{tsin (xt)}{{(x^{2} + t^{2})}^{2}} dt (x > 0)$ $calculate f^{^{'}} (x)$

Question Number 131049 Answers: 1 Comments: 0

let f(x)=∫_0 ^∞ ((cos(xt))/(x^2 +t^2 ))dt calculate ∫_0 ^1 f(x)dx

$let f (x) = \int_{0}^{\infty} \frac{\cos (xt)}{x^{2} + t^{2}} dt calculate \int_{0}^{1} f (x) dx$

Question Number 130979 Answers: 4 Comments: 3

φ =∫_0 ^( ∞) log^2 (x)sin(x^2 )dx=? i had solved that already and: answ : = −((π^2 (√(2π)) )/(32))

$ϕ = \int_{0}^{\infty} {l o g}^{2} (x) s i n (x^{2}) d x = ?$ $i h a d s o l v e d t h a t a l r e a d y a n d :$ $a n s w : = - \frac{π^{2} \sqrt{2 π}}{32}$

Pg 95 Pg 96 Pg 97 Pg 98 Pg 99 Pg 100 Pg 101 Pg 102 Pg 103 Pg 104

Contact: info@tinkutara.com