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

The integral from-1 to 1 of (3x^2-2x+4) is 10

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

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

10

Solution steps

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

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

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

\int_{- 1}^{1} 4 d x = 8

= 2 - 0 + 8

Simplify

= 10

\int_{0}^{2} 4 x^{4} d x

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

\int_{1}^{3} 3 x^{2} - 10 x + 5 d x

\int_{0}^{2} 2 2 x d x

\int_{7}^{10} \frac{x}{7} - \frac{7}{x} d x

What is the integral from-1 to 1 of (3x^2-2x+4) ?
The integral from-1 to 1 of (3x^2-2x+4) is 10