What is the integral from 0 to 2 of (5x^2-6x+7) ?

The integral from 0 to 2 of (5x^2-6x+7) is 46/3

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integral from 0 to 2 of (5x^2-6x+7)

\int_{0}^{2} (5 x^{2} - 6 x + 7) d x

\frac{46}{3}

Decimal

15.33333 \dots

Solution steps

\int_{0}^{2} 5 x^{2} - 6 x + 7 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}^{2} 5 x^{2} d x - \int_{0}^{2} 6 x d x + \int_{0}^{2} 7 d x

\int_{0}^{2} 5 x^{2} d x = \frac{40}{3}

\int_{0}^{2} 6 x d x = 12

\int_{0}^{2} 7 d x = 14

= \frac{40}{3} - 12 + 14

Simplify

\frac{40}{3} - 12 + 14 : \frac{46}{3}

= \frac{46}{3}

\int_{0}^{6} \frac{185}{( x + 1 ) ^{3}} d x

\int_{0}^{4} r d r

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

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

What is the integral from 0 to 2 of (5x^2-6x+7) ?
The integral from 0 to 2 of (5x^2-6x+7) is 46/3