DonMath

What is calculus

what is pie

Find x and y

You are welcome

```

1+x
log|---|
|7!-1000|₁ 1-x
Ω=|-------|∫--------
| π² |⁰ x√[1-x²]


recall that,

1 1+x
tanh⁻¹x=--log|----|
2 1-x

so,


₁ tanh⁻¹x
Ω₁=2∫---------dx
⁰ x√[1-x²]

let

u=tanh⁻¹x

x=tanhu, dx=sexh²udu

when x=1 u=0

x=0 u=∞

∞ usech²udu
Ω₁=2∫ --------------
⁰tanhu√[1-tanh²u]


∞ usechudu
Ω₁=2∫ --------
⁰ tanhu

∞ udu
Ω₁=2∫ -----
⁰ sinhu

Recall,

sinhu=[eᵘ-e⁻ᵘ]/₂

∞ udu
Ω₁=4∫ -----
⁰ eᵘ-e⁻ᵘ

∞ ue⁻udu
Ω₁=4∫ ------
⁰ 1-e⁻ᵘ

∞ ∞
Ω₁=4Σ ∫ ue⁻²ᵘⁿ⁻ᵘdu
ⁿ⁻⁰ ⁰

This is laplase of u where

s=2n+1[from -u[2n+1]

∞ 1
Ω₁=4Σ -----
ⁿ⁻⁰ [2n+1]¹⁺¹

∞ 1
Ω₁=4Σ -------
ⁿ⁻⁰ 4[n+¹/₂]²

∞ 1 π²
Ω₁=Σ -------=---
ⁿ⁻⁰ [n+¹/₂]² 2

but

7!-1000
Ω=-------×Ω₁
π²

7!-1000 π²
Ω=-------×---
π² 2

4040
Ω=----=2020
2

Hᵃᵖᵖʸ Nᵉʷ Month!..

Donmath[Wᵃᵗᵉʳ Fᵒʳᵐᵉʳ].

THANK YOU```✊

If a man has 6 and 4 different ties and shirts respectively, how many different combinations can he wear

ANS: 6×4=24