What is the integral from 0 to 7 of |sqrt(4x+5)-x| ?

The integral from 0 to 7 of |sqrt(4x+5)-x| is -1/2+(250-5sqrt(5)-33sqrt(33))/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 7 of |sqrt(4x+5)-x|

\int_{0}^{7} 4 x + 5 - x d x

- \frac{1}{2} + \frac{250 - 5 5 - 33 33}{6}

Decimal Notation

7.70818 \dots

Solution steps

\int_{0}^{7} 4 x + 5 - x d x

Eliminate Absolutes

= \int_{0}^{5} 4 x + 5 - x d x + \int_{5}^{7} - 4 x + 5 + x d x

\int_{0}^{5} 4 x + 5 - x d x = \frac{5 ( 25 - 5 )}{6} - \frac{25}{2}

\int_{5}^{7} - 4 x + 5 + x d x = - \frac{33 33 - 125}{6} + 12

= \frac{5 ( 25 - 5 )}{6} - \frac{25}{2} - \frac{33 33 - 125}{6} + 12

Combine the fractions

12 - \frac{25}{2} : - \frac{1}{2}

Combine the fractions

\frac{5 ( 25 - 5 )}{6} - \frac{33 33 - 125}{6} : \frac{250 - 5 5 - 33 33}{6}

= - \frac{1}{2} + \frac{250 - 5 5 - 33 33}{6}

f (x) = \frac{x ^{2} - 4}{x}

\int 1 + \frac{1}{4} sin^{2} (x) d x

\int e^{x} e^{x} + 1 d x

x \to 6 lim (x^{2} - 3 x)

\int (\frac{1}{x - 1}) d x

What is the integral from 0 to 7 of |sqrt(4x+5)-x| ?
The integral from 0 to 7 of |sqrt(4x+5)-x| is -1/2+(250-5sqrt(5)-33sqrt(33))/6