What is the integral from-1 to 0 of (3x^2-2x-1/2) ?

The integral from-1 to 0 of (3x^2-2x-1/2) is 3/2

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integral from-1 to 0 of (3x^2-2x-1/2)

\int_{- 1}^{0} (3 x^{2} - 2 x - \frac{1}{2}) d x

\frac{3}{2}

Decimal

1.5

Solution steps

\int_{- 1}^{0} 3 x^{2} - 2 x - \frac{1}{2} 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} 3 x^{2} d x - \int_{- 1}^{0} 2 x d x - \int_{- 1}^{0} \frac{1}{2} d x

\int_{- 1}^{0} 3 x^{2} d x = 1

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

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

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

Simplify

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

= \frac{3}{2}

What is the integral from-1 to 0 of (3x^2-2x-1/2) ?
The integral from-1 to 0 of (3x^2-2x-1/2) is 3/2