In lighter vain!!

Well, junta complain that I don't post frequently enuff. So thats why I reverted to something that really interests me Mathematics.Well, junta don't yawn coz what u shall c is not the number-crunching stuff but mathematics in a lighter vain. Mathematics largely perceived as a arcane and pristine stuff, which is absolute and don't defer in any circumstances ; but few realize that maths can be pure fun if u can see the funny side of mathematics.mathematical fallacies are very commonplace and can be very entertaining stuff.For example this one which I came to know as early as class six.It was pretty baffling to me that time but u just cant ignore the craftiness of the problem. OK here we go!!

a = b [ let us assume]

ab = b² [ Multiplying both sides by b]

ab – a² = b²- a² [ Subtracting both sides by a² ]

a(b-a) = (b-a)(b+a) [ simplifying]

a = b + a

Let us say a = b = 1 conforming to our initial hypothesis

So, 1 = 1+ 1

i.e 1 = 2 !!!!!! [ Is that possible ???!!@@# ]

Well, if u have an answer do write it in my scrap. Well, now we'll have some twist with mathematical symbols. Here it goes

∫ e^x = ∫ uⁿ

I know that this is mathematically outrageous , a complete blasphemy of integral calculus and a complete nonsense when it comes to its mathematical integrity. But however here is some thing hidden in this ........ a little funny something which an inquisitive and shrewed mind can only see. See between the lines and decipher it to me!!