What is the integral from-1 to 1 of (|x|-1/2)^2 ?

The integral from-1 to 1 of (|x|-1/2)^2 is 1/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 1 of (|x|-1/2)^2

\int_{- 1}^{1} (∣ x ∣ - \frac{1}{2})^{2} d x

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

\int_{- 1}^{1} (∣ x ∣ - \frac{1}{2})^{2} d x

Eliminate Absolutes

= \int_{- 1}^{0} (- x - \frac{1}{2})^{2} d x + \int_{0}^{1} (x - \frac{1}{2})^{2} d x

\int_{- 1}^{0} (- x - \frac{1}{2})^{2} d x = \frac{1}{12}

\int_{0}^{1} (x - \frac{1}{2})^{2} d x = \frac{1}{12}

= \frac{1}{12} + \frac{1}{12}

Simplify

\frac{1}{12} + \frac{1}{12} : \frac{1}{6}

= \frac{1}{6}

\int_{1}^{6} (- x^{2} + 7 x - 6) d x

\int_{0}^{20} (840 - 42 x) d x

\int_{0}^{2 π} - 4 sin^{2} (θ) d θ

\int_{3}^{4} x^{5} d x

\int_{0}^{3} (\frac{1}{2} x^{2} - 1) d x

What is the integral from-1 to 1 of (|x|-1/2)^2 ?
The integral from-1 to 1 of (|x|-1/2)^2 is 1/6