Question-93227

Question Number 93227 by Ajao yinka last updated on 11/May/20

Commented by prakash jain last updated on 12/May/20

2 \int_{- \infty}^{+ \infty} x^{4} δ (1 + x + x^{2} + x^{3}) d x = 2 \times (\frac{2}{4}) = 1

\frac{1}{2 + \frac{1}{2 + \frac{1}{2 + . .}}} (it is covergent . i will skip proof) w

\frac{1}{2 + x} = x \Rightarrow x^{2} + 2 x - 1 = 0

x = \frac{- 2 \pm \sqrt{8}}{2} = \sqrt{2} - 1

So the given expression becomes

1 + \sqrt{2} - 1 + \sinh^{- 1} (\underset{n = 0}{\sum^{\infty}} \frac{1}{2 n! (2 n + 1)}) - 1 =>

= \sqrt{2} - 1 + \sinh^{- 1} (\underset{n = 0}{\sum^{\infty}} \frac{1}{2 n! (2 n + 1)}) = 0

= \sqrt{2} - 1 + \sinh^{- 1} (\sinh 1)

= \sqrt{2}

It is not equal to zero as claimed

in question . Can you please recheck

quesstiin

Commented by prakash jain last updated on 12/May/20

For the proof of integral in last part. please see q93225

Commented by Ajao yinka last updated on 14/May/20

You're wrong

Commented by prakash jain last updated on 14/May/20

Do you also want go explain on what

part of answer is wrong ?