What is the integral from 0 to 3 of 3x+4-(x^2+4) ?

The integral from 0 to 3 of 3x+4-(x^2+4) is 9/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 3 of 3x+4-(x^2+4)

\int_{0}^{3} 3 x + 4 - (x^{2} + 4) d x

\frac{9}{2}

Decimal

4.5

Solution steps

\int_{0}^{3} 3 x + 4 - (x^{2} + 4) d x

Simplify

= \int_{0}^{3} - x^{2} + 3 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}^{3} x^{2} d x + \int_{0}^{3} 3 x d x

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 3 x d x = \frac{27}{2}

= - 9 + \frac{27}{2}

Simplify

- 9 + \frac{27}{2} : \frac{9}{2}

= \frac{9}{2}

What is the integral from 0 to 3 of 3x+4-(x^2+4) ?
The integral from 0 to 3 of 3x+4-(x^2+4) is 9/2