What is the integral from 0 to 9 of sqrt(x)-1/2 x ?

The integral from 0 to 9 of sqrt(x)-1/2 x is -9/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 9 of sqrt(x)-1/2 x

\int_{0}^{9} x - \frac{1}{2} x d x

- \frac{9}{4}

Decimal

- 2.25

Solution steps

\int_{0}^{9} x - \frac{1}{2} 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

= \int_{0}^{9} x d x - \int_{0}^{9} \frac{1}{2} x d x

\int_{0}^{9} x d x = 18

\int_{0}^{9} \frac{1}{2} x d x = \frac{81}{4}

= 18 - \frac{81}{4}

Simplify

18 - \frac{81}{4} : - \frac{9}{4}

= - \frac{9}{4}

\int_{1}^{5} 6 d x

\int_{- 1}^{0} e^{x + 1} d x

\int_{7}^{10} (x - 8)^{2} d x

\int_{0}^{1} 6 x^{2} 1 - x^{3} d x

\int_{0}^{1} \frac{e ^{2 x} - 1}{e ^{x}} d x

What is the integral from 0 to 9 of sqrt(x)-1/2 x ?
The integral from 0 to 9 of sqrt(x)-1/2 x is -9/4