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

The integral from-1 to 2 of (x^3+5x^2-1) is 63/4

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integral from-1 to 2 of (x^3+5x^2-1)

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

\frac{63}{4}

Decimal Notation

15.75

Solution steps

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

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

\int_{- 1}^{2} 5 x^{2} d x = 15

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

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

Simplify

\frac{15}{4} + 15 - 3 : \frac{63}{4}

= \frac{63}{4}

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What is the integral from-1 to 2 of (x^3+5x^2-1) ?
The integral from-1 to 2 of (x^3+5x^2-1) is 63/4