What is the integral from-1 to 1/2 of 4x^2-x+1/2 ?

The integral from-1 to 1/2 of 4x^2-x+1/2 is 21/8

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integral from-1 to 1/2 of 4x^2-x+1/2

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

\frac{21}{8}

Decimal

2.625

Solution steps

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

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

\int_{- 1}^{\frac{1}{2}} x d x = - \frac{3}{8}

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

= \frac{3}{2} - (- \frac{3}{8}) + \frac{3}{4}

Simplify

\frac{3}{2} - (- \frac{3}{8}) + \frac{3}{4} : \frac{21}{8}

= \frac{21}{8}

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What is the integral from-1 to 1/2 of 4x^2-x+1/2 ?
The integral from-1 to 1/2 of 4x^2-x+1/2 is 21/8