What is the integral from-4 to 0 of x^3-x^2-14x ?

The integral from-4 to 0 of x^3-x^2-14x is 80/3

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integral from-4 to 0 of x^3-x^2-14x

\int_{- 4}^{0} x^{3} - x^{2} - 14 x d x

\frac{80}{3}

Decimal

26.66666 \dots

Solution steps

\int_{- 4}^{0} x^{3} - x^{2} - 14 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}^{0} x^{3} d x - \int_{- 4}^{0} x^{2} d x - \int_{- 4}^{0} 14 x d x

\int_{- 4}^{0} x^{3} d x = - 64

\int_{- 4}^{0} x^{2} d x = \frac{64}{3}

\int_{- 4}^{0} 14 x d x = - 112

= - 64 - \frac{64}{3} - (- 112)

Simplify

- 64 - \frac{64}{3} - (- 112) : \frac{80}{3}

= \frac{80}{3}

\int_{0}^{2} x + 5 d x

\int_{π}^{x} t^{3} sin^{2} (t) d t

\int_{0}^{2} \frac{y ^{3}}{1 + y ^{4}} d y

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

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

What is the integral from-4 to 0 of x^3-x^2-14x ?
The integral from-4 to 0 of x^3-x^2-14x is 80/3