What is the integral from 0 to 1 of xsqrt(5x+4) ?

The integral from 0 to 1 of xsqrt(5x+4) is 506/375

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 xsqrt(5x+4)

\int_{0}^{1} x 5 x + 4 d x

\frac{506}{375}

Decimal

1.34933 \dots

Solution steps

\int_{0}^{1} x 5 x + 4 d x

Apply u-substitution

= \int_{4}^{9} \frac{u ( u - 4 )}{25} d u

Take the constant out:

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

= \frac{1}{25} \cdot \int_{4}^{9} u (u - 4) d u

Expand

u (u - 4) : u^{\frac{3}{2}} - 4 u

= \frac{1}{25} \cdot \int_{4}^{9} u^{\frac{3}{2}} - 4 u d u

Apply the Sum Rule:

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

= \frac{1}{25} (\int_{4}^{9} u^{\frac{3}{2}} d u - \int_{4}^{9} 4 u d u)

\int_{4}^{9} u^{\frac{3}{2}} d u = \frac{422}{5}

\int_{4}^{9} 4 u d u = \frac{152}{3}

= \frac{1}{25} (\frac{422}{5} - \frac{152}{3})

Simplify

\frac{1}{25} (\frac{422}{5} - \frac{152}{3}) : \frac{506}{375}

= \frac{506}{375}

What is the integral from 0 to 1 of xsqrt(5x+4) ?
The integral from 0 to 1 of xsqrt(5x+4) is 506/375