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

The integral from-1 to 2 of (x^2+x+1) is 15/2

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

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

\frac{15}{2}

Decimal

7.5

Solution steps

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

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

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

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

= 3 + \frac{3}{2} + 3

Simplify

3 + \frac{3}{2} + 3 : \frac{15}{2}

= \frac{15}{2}

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What is the integral from-1 to 2 of (x^2+x+1) ?
The integral from-1 to 2 of (x^2+x+1) is 15/2