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

The integral from-1 to 2 of (x^3+3)-(x-1) is 57/4

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integral from-1 to 2 of (x^3+3)-(x-1)

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

\frac{57}{4}

Decimal

14.25

Solution steps

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

Simplify

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

\int_{- 1}^{2} x^{3} d x = \frac{15}{4}

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

\int_{- 1}^{2} 4 d x = 12

= \frac{15}{4} - \frac{3}{2} + 12

Simplify

\frac{15}{4} - \frac{3}{2} + 12 : \frac{57}{4}

= \frac{57}{4}

What is the integral from-1 to 2 of (x^3+3)-(x-1) ?
The integral from-1 to 2 of (x^3+3)-(x-1) is 57/4