What is the integral from-1 to 3 of (3x-5)(x+2) ?

The integral from-1 to 3 of (3x-5)(x+2) is -8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-1 to 3 of (3x-5)(x+2)

\int_{- 1}^{3} (3 x - 5) (x + 2) d x

- 8

Solution steps

\int_{- 1}^{3} (3 x - 5) (x + 2) d x

Expand

(3 x - 5) (x + 2) : 3 x^{2} + x - 10

= \int_{- 1}^{3} 3 x^{2} + x - 10 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_{- 1}^{3} 3 x^{2} d x + \int_{- 1}^{3} x d x - \int_{- 1}^{3} 10 d x

\int_{- 1}^{3} 3 x^{2} d x = 28

\int_{- 1}^{3} x d x = 4

\int_{- 1}^{3} 10 d x = 40

= 28 + 4 - 40

Simplify

= - 8

\int_{2}^{4} 8 - 2 x d x

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

\int_{0}^{0.1} 600 x d x

\int_{3}^{6} g (x) d x

\int_{- 1}^{0} 4 d x

What is the integral from-1 to 3 of (3x-5)(x+2) ?
The integral from-1 to 3 of (3x-5)(x+2) is -8