What is the integral from 0 to 1 of (5x^2-6x+6) ?

The integral from 0 to 1 of (5x^2-6x+6) is 14/3

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integral from 0 to 1 of (5x^2-6x+6)

\int_{0}^{1} (5 x^{2} - 6 x + 6) d x

\frac{14}{3}

Decimal Notation

4.66666 \dots

Solution steps

\int_{0}^{1} 5 x^{2} - 6 x + 6 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_{0}^{1} 5 x^{2} d x - \int_{0}^{1} 6 x d x + \int_{0}^{1} 6 d x

\int_{0}^{1} 5 x^{2} d x = \frac{5}{3}

\int_{0}^{1} 6 x d x = 3

\int_{0}^{1} 6 d x = 6

= \frac{5}{3} - 3 + 6

Simplify

\frac{5}{3} - 3 + 6 : \frac{14}{3}

= \frac{14}{3}

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

\int_{0}^{1} cos (πn x) d x

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

\int_{1}^{6} ∣ x - 3 ∣ d x

\int_{0}^{x} e^{- t^{6}} d t

What is the integral from 0 to 1 of (5x^2-6x+6) ?
The integral from 0 to 1 of (5x^2-6x+6) is 14/3