Question

`int_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e^2x dx = ?

Options

• e²

• e + 1

• e

• e - 1

Answer 1

e - 1

Explanation:

We know that,

e^-x = `1 - x/(1!) + x^2/(2!) - x^3/(3!)` + .... upto ∞

∴ I = `int_0^1 "e"^(- x) * "e"^"2x"`dx

I = `int_0^1 "e"^x`dx

I = `["e"^x]_0^1 = "e"^1 - "e"^0` = e - 1