What is the integral from-1 to 3 of x^3-4x^2+5 ?

The integral from-1 to 3 of x^3-4x^2+5 is 8/3

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^3-4x^2+5

\int_{- 1}^{3} x^{3} - 4 x^{2} + 5 d x

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

\int_{- 1}^{3} x^{3} - 4 x^{2} + 5 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} 4 x^{2} d x + \int_{- 1}^{3} 5 d x

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

\int_{- 1}^{3} 4 x^{2} d x = \frac{112}{3}

\int_{- 1}^{3} 5 d x = 20

= 20 - \frac{112}{3} + 20

Simplify

20 - \frac{112}{3} + 20 : \frac{8}{3}

= \frac{8}{3}

\int_{0}^{1} t 1 + 16 t^{2} d t

\int_{0}^{6} \frac{2 x}{x ^{2} + 1} d x

\int_{3}^{5} \frac{1}{2 x - 6} d x

\int_{0}^{π} sin (d) x d x

\int_{- 2}^{3} - 3 ∣ x ∣ d x

What is the integral from-1 to 3 of x^3-4x^2+5 ?
The integral from-1 to 3 of x^3-4x^2+5 is 8/3