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

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

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

\int_{- 1}^{1} \frac{3 x ^{2} - 5 x + 1}{4} d x

1

Solution steps

\int_{- 1}^{1} \frac{3 x ^{2} - 5 x + 1}{4} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{- 1}^{1} 3 x^{2} - 5 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

= \frac{1}{4} (\int_{- 1}^{1} 3 x^{2} d x - \int_{- 1}^{1} 5 x d x + \int_{- 1}^{1} 1 d x)

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

\int_{- 1}^{1} 5 x d x = 0

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

= \frac{1}{4} (2 - 0 + 2)

Simplify

\frac{1}{4} (2 - 0 + 2) : 1

= 1

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