What is the integral from 0 to 1 of 2(x+y) ?

The integral from 0 to 1 of 2(x+y) is 2y+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 1 of 2(x+y)

\int_{0}^{1} 2 (x + y) d x

2 y + 1

Solution steps

\int_{0}^{1} 2 (x + y) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{1} y + x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{1} y d x = y

\int_{0}^{1} x d x = \frac{1}{2}

= 2 (y + \frac{1}{2})

Simplify

2 (y + \frac{1}{2}) : 2 y + 1

= 2 y + 1

What is the integral from 0 to 1 of 2(x+y) ?
The integral from 0 to 1 of 2(x+y) is 2y+1