What is the integral from 0 to 3 of (6+6y-y^2) ?

The integral from 0 to 3 of (6+6y-y^2) is 36

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 3 of (6+6y-y^2)

\int_{0}^{3} (6 + 6 y - y^{2}) d y

36

Solution steps

\int_{0}^{3} 6 + 6 y - y^{2} d y

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} 6 d y + \int_{0}^{3} 6 y d y - \int_{0}^{3} y^{2} d y

\int_{0}^{3} 6 d y = 18

\int_{0}^{3} 6 y d y = 27

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

= 18 + 27 - 9

Simplify

= 36

\int_{- 2}^{1} x^{3} + x d x

\int_{1}^{4} (9 x - 6 x) d x

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

\int_{5}^{9} (5 - x) (x - 9) d x

\int_{0}^{\frac{3}{7}} 3 x - 7 x^{2} d x

What is the integral from 0 to 3 of (6+6y-y^2) ?
The integral from 0 to 3 of (6+6y-y^2) is 36