$\int\limits_{-1}^{1} e^{|x|} dx = $

CUET Preparation Today

Start Free Mocks

Home Questions TWM2F6VVUE

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Determinants

Question:

$\int\limits_{-1}^{1} e^{|x|} dx = $

Options:

2(e^-1 - 1)

2(e + 1)

e - 1

2(e - 1)

Correct Answer:

2(e - 1)

Explanation:

$I = \int\limits_{-1}^{1} e^{|x|} dx = ?$

so $e^{|x|}$ is a symmetric function (even function)

⇒ $I = 2 \int\limits_0^1 e^x ~dx$ for x > 0 ⇒ $e^{|x|} = e^y$

⇒ $I = 2 \int\limits_0^1 e^x ~dx$

= $2[e^x]_0^1$

= 2[e¹ - 1]

= 2e - 2