What is the integral from-4 to 3 of (x^3+x^2-6x)-6x ?

The integral from-4 to 3 of (x^3+x^2-6x)-6x is 343/12

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-4 to 3 of (x^3+x^2-6x)-6x

\int_{- 4}^{3} (x^{3} + x^{2} - 6 x) - 6 x d x

\frac{343}{12}

Decimal Notation

28.58333 \dots

Solution steps

\int_{- 4}^{3} x^{3} + x^{2} - 6 x - 6 x d x

Simplify

= \int_{- 4}^{3} x^{3} + x^{2} - 12 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_{- 4}^{3} x^{3} d x + \int_{- 4}^{3} x^{2} d x - \int_{- 4}^{3} 12 x d x

\int_{- 4}^{3} x^{3} d x = - \frac{175}{4}

\int_{- 4}^{3} x^{2} d x = \frac{91}{3}

\int_{- 4}^{3} 12 x d x = - 42

= - \frac{175}{4} + \frac{91}{3} - (- 42)

Simplify

- \frac{175}{4} + \frac{91}{3} - (- 42) : \frac{343}{12}

= \frac{343}{12}

y = \frac{1}{x ^{5}}

\int 14 d x

\int 2 π x^{3} sin (x) d x

\frac{\partial}{\partial x} (\frac{y ^{3}}{x ^{2} + y ^{2}})

x \frac{d y}{d x} + y = x^{3}

What is the integral from-4 to 3 of (x^3+x^2-6x)-6x ?
The integral from-4 to 3 of (x^3+x^2-6x)-6x is 343/12