What is the integral from-1 to 0 of-3-x^3+3-x ?

The integral from-1 to 0 of-3-x^3+3-x is 3/4

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integral from-1 to 0 of-3-x^3+3-x

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

\frac{3}{4}

Decimal

0.75

Solution steps

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

Simplify

= \int_{- 1}^{0} - x^{3} - 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_{- 1}^{0} x^{3} d x - \int_{- 1}^{0} x d x

\int_{- 1}^{0} x^{3} d x = - \frac{1}{4}

\int_{- 1}^{0} x d x = - \frac{1}{2}

= - (- \frac{1}{4}) - (- \frac{1}{2})

Simplify

- (- \frac{1}{4}) - (- \frac{1}{2}) : \frac{3}{4}

= \frac{3}{4}

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

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

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

\int_{1}^{x} u \cdot ln (u) d u

What is the integral from-1 to 0 of-3-x^3+3-x ?
The integral from-1 to 0 of-3-x^3+3-x is 3/4