∫ n√( 1 n ^ 2 ) dn 1 n ^ 2 =t 2ndn=dt ndn= dt 2 ∫ t ^ 1/2 dt 2 #160; = 1 2 t ^ 3/2 3/2 = 1 3 ( 1 n ^ 2 ) #160; ^ 3/2 ...

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Functions

∫ n√ 1- n 2 d...

Question

$\int n \sqrt{1 - n^{2}} d n$

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Solution

$\int n \sqrt{1 - n^{2}} d n 1 - n^{2} = t$
$- 2 n d n = d t$
$n d n = \frac{- d t}{2}$
$- \int \frac{t^{1 / 2} d t}{2} = - \frac{1}{2} \frac{t^{3 / 2}}{3 / 2} = \frac{- 1}{3} {(1 - n^{2})}^{3 / 2}$

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Similar questions

lim n \to \infty (\frac{1}{\sqrt{n} \sqrt{n + 1}} + \frac{1}{\sqrt{n} \sqrt{n + 2}} + . . . . . . . \frac{1}{\sqrt{n} \sqrt{n + n}})

n \in N

n

\frac{1}{1. (n - 1)!} + \frac{1}{3! . (n - 3)!} + \frac{1}{5! . (n - 5)!} + . . . . . . + \frac{1}{(n - 1)! 1!} =

n \in N

\frac{1}{1! \cdot (n - 1)!}

\frac{1}{3! \cdot (n - 3)!}

\frac{1}{5! \cdot (n - 5)!}

\frac{1}{(n - 1)! 1!}

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦

A^{n} = ⎡ ⎢ ⎣ \begin{matrix} 3^{n - 1} & 3^{n - 1} & 3^{n - 1} 3^{n - 1} & 3^{n - 1} & 3^{n - 1} 3^{n - 1} & 3^{n - 1} & 3^{n - 1} \end{matrix} ⎤ ⎥ ⎦, n \in N

(1 - \frac{1}{n + 1}) + (1 - \frac{2}{n + 1}) + (1 - \frac{3}{n + 1}) + . . . . . . . . . . . . . . + (1 - \frac{n}{n + 1})

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