What is the integral from-1 to 3 of x^3-3x^2-1 ?

The integral from-1 to 3 of x^3-3x^2-1 is -12

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 3 of x^3-3x^2-1

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

- 12

Solution steps

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

\int_{- 1}^{3} x^{3} d x = 20

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

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

= 20 - 28 - 4

Simplify

= - 12

\int_{0}^{2} \frac{x}{4 4 - x ^{2}} d x

\int_{0}^{1} 3 k - k x d x

\int_{- 4}^{4} \frac{y}{16 - y ^{2}} d y

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

\int_{0}^{3} y e^{- x y} d y

What is the integral from-1 to 3 of x^3-3x^2-1 ?
The integral from-1 to 3 of x^3-3x^2-1 is -12