Question and Answers Forum

IntegrationQuestion and Answers: Page 123

Question Number 122349 Answers: 1 Comments: 1

Find the polynomial P(x) of least degree that has a maximum equal to 6 at x=1 and minimum equal to 2 at x=3.

$Find the polynomial P (x) of least degree$ $that has a maximum equal to 6 at x = 1$ $and minimum equal to 2 at x = 3 .$

Question Number 122330 Answers: 2 Comments: 0

...advanced calculus... prove that : Re(∫_0 ^( (π/2)) sin^3 (x)ln(ln(cos(x)))dx) =^? ((ln(3)−2γ)/3) ✓

$. . . a d v a n c e d c a l c u l u s . . .$ $p r o v e t h a t :$ $R e (\int_{0}^{\frac{π}{2}} {s i n}^{3} (x) l n (l n (c o s (x))) d x)$ $\overset{?}{=} \frac{l n (3) - 2 γ}{3} ✓$

Question Number 122323 Answers: 1 Comments: 1

calculate A_n =∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)....(x^2 +n))) wth n integr natural and n≥1

$calculate A_{n} = \int_{0}^{\infty} \frac{dx}{(x^{2} + 1) (x^{2} + 2) . . . . (x^{2} + n)}$ $wth n integr natural and n ⩾ 1$

Question Number 122298 Answers: 1 Comments: 0

...nice calculus... prove that : Σ_(n=1 ) ^∞ {((ζ(2n+1)−1)/(n+1))}=−γ+ln(2)✓ ..m.n.1970..

$. . . n i c e c a l c u l u s . . .$ $p r o v e t h a t :$ $\underset{n = 1}{\sum^{\infty}} {\frac{ζ (2 n + 1) - 1}{n + 1}} = - γ + l n (2) ✓$ $. . m . n . 1970 . .$

Question Number 122290 Answers: 1 Comments: 1

... nice calculus... calculate :: Ω=∫_0 ^( 1) x^2 (ψ(1+x)−ψ(2−x))dx=??? .m.n.1970.

$. . . n i c e c a l c u l u s . . .$ $c a l c u l a t e ::$ $Ω = \int_{0}^{1} x^{2} (ψ (1 + x) - ψ (2 - x)) d x = ? ? ?$ $. m . n . 1970 .$

Question Number 122274 Answers: 2 Comments: 0

∫ ((√(1−(√x)))/( (√(1+(√x))))) dx ?

$\int \frac{\sqrt{1 - \sqrt{x}}}{\sqrt{1 + \sqrt{x}}} d x ?$

Question Number 122205 Answers: 1 Comments: 2

find ∫ (dx/(x(x+1)(√(x^2 +x))))

$find \int \frac{dx}{x (x + 1) \sqrt{x^{2} + x}}$

Question Number 122186 Answers: 2 Comments: 0

Obtain a reduction formulae for I_n = ∫_0 ^1 (ln x)^n dx find I_2 = ∫_0 ^1 (ln x)^2 dx

$Obtain a reduction formulae for$ $I_{n} = \underset{0}{\int^{1}} {(\ln x)}^{n} d x$ $find I_{2} = \underset{0}{\int^{1}} {(\ln x)}^{2} d x$

Question Number 122160 Answers: 1 Comments: 0

Question Number 122159 Answers: 3 Comments: 0

... nice calculus... prove that:: Ω=∫_0 ^( (π/2)) {tan^(−1) (ptan(x))−tan^(−1) (qtan(x))}(tan(x)+cot(x))dx =(π/2) log((p/q)) ( p , q >0 ) m.n.

$. . . n i c e c a l c u l u s . . .$ $p r o v e t h a t ::$ $Ω = \int_{0}^{\frac{π}{2}} {{t a n}^{- 1} (p t a n (x)) - {t a n}^{- 1} (q t a n (x))} (t a n (x) + c o t (x)) d x$ $= \frac{π}{2} l o g (\frac{p}{q}) (p, q > 0)$ $m . n .$

Question Number 122157 Answers: 2 Comments: 1

find ∫_(−1) ^1 (√(1+x^4 ))dx

$find \int_{- 1}^{1} \sqrt{1 + x^{4}} dx$

Question Number 122137 Answers: 1 Comments: 0

Question Number 122120 Answers: 2 Comments: 0

∫_0 ^3 (1/( (√y))).e^y dy

$\underset{0}{\int^{3}} \frac{1}{\sqrt{y}} . e^{y} d y$

Question Number 122109 Answers: 2 Comments: 0

Question Number 122108 Answers: 1 Comments: 0

∫_1 ^2 ((ln (x))/x^2 ) dx ?

$\underset{1}{\int^{2}} \frac{\ln (x)}{x^{2}} d x ?$

Question Number 122098 Answers: 1 Comments: 1

Question Number 122044 Answers: 0 Comments: 3

Question Number 122035 Answers: 1 Comments: 0

...nice calculus... prove that : ∫_0 ^( 1) ((ln^2 (1+x))/x)dx=^(??) ((ζ(3))/4) .m.n.

$. . . n i c e c a l c u l u s . . .$ $p r o v e t h a t :$ $\int_{0}^{1} \frac{{l n}^{2} (1 + x)}{x} d x \overset{? ?}{=} \frac{ζ (3)}{4}$ $. m . n .$

Question Number 121972 Answers: 1 Comments: 0

∫_0 ^( ∞) e^(−x^2 ) cos(5x)dx

$\int_{0}^{\infty} e^{- x^{2}} \cos (5 x) dx$

Question Number 121965 Answers: 2 Comments: 0

∫_4 ^9 ((ℓn (x))/( (√x))) dx ?

$\underset{4}{\int^{9}} \frac{ℓ n (x)}{\sqrt{x}} d x ?$

Question Number 121962 Answers: 2 Comments: 0

∫_0 ^1 (dx/( ((x^2 −x^3 ))^(1/(3 )) )) ?

$\underset{0}{\int^{1}} \frac{d x}{\sqrt[3]{x^{2} - x^{3}}} ?$

Question Number 121928 Answers: 1 Comments: 2

Σ_(n=0) ^∞ ((1/(12n+1))+(1/(12n+5))−(1/(12n+7))−(1/(12n+11))) Problem source : Brilliant.Org

$\underset{n = 0}{\sum^{\infty}} (\frac{1}{12 n + 1} + \frac{1}{12 n + 5} - \frac{1}{12 n + 7} - \frac{1}{12 n + 11})$ $P r o b l e m s o u r c e : B r i l l i a n t . O r g$

Question Number 121887 Answers: 2 Comments: 2

Question Number 121886 Answers: 2 Comments: 1

Question Number 121875 Answers: 2 Comments: 0

Question Number 121862 Answers: 1 Comments: 0

1)explicite f(a)=∫_0 ^∞ ((t^(a−1) lnt)/(1+t))dt with 0<a<1 2)calculate ∫_0 ^∞ ((lnt)/((1+t)(√t)))dt

$1) e x p l i c i t e f (a) = \int_{0}^{\infty} \frac{t^{a - 1} l n t}{1 + t} d t$ $w i t h 0 < a < 1$ $2) c a l c u l a t e \int_{0}^{\infty} \frac{l n t}{(1 + t) \sqrt{t}} d t$

Pg 118 Pg 119 Pg 120 Pg 121 Pg 122 Pg 123 Pg 124 Pg 125 Pg 126 Pg 127

Contact: info@tinkutara.com