What is the integral from 2 to 4 of (2(1+x))/(27) ?

The integral from 2 to 4 of (2(1+x))/(27) is 16/27

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 4 of (2(1+x))/(27)

\int_{2}^{4} \frac{2 ( 1 + x )}{27} d x

\frac{16}{27}

Decimal Notation

0.59259 \dots

Solution steps

\int_{2}^{4} \frac{2 ( 1 + x )}{27} d x

Take the constant out:

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

= \frac{2}{27} \cdot \int_{2}^{4} 1 + 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

= \frac{2}{27} (\int_{2}^{4} 1 d x + \int_{2}^{4} x d x)

\int_{2}^{4} 1 d x = 2

\int_{2}^{4} x d x = 6

= \frac{2}{27} (2 + 6)

Simplify

\frac{2}{27} (2 + 6) : \frac{16}{27}

= \frac{16}{27}

\int_{1}^{2} - x^{2} + 4 d x

\int_{0}^{2} e^{- x^{2}} x d x

\int_{1}^{3} \frac{x ^{3}}{x} d x

\int_{0}^{\frac{π}{4}} x \cdot sin (x) d x

What is the integral from 2 to 4 of (2(1+x))/(27) ?
The integral from 2 to 4 of (2(1+x))/(27) is 16/27