What is the integral from 0 to 2 of x^3-2x^2+10x ?

The integral from 0 to 2 of x^3-2x^2+10x is 56/3

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integral from 0 to 2 of x^3-2x^2+10x

\int_{0}^{2} x^{3} - 2 x^{2} + 10 x d x

\frac{56}{3}

Decimal

18.66666 \dots

Solution steps

\int_{0}^{2} x^{3} - 2 x^{2} + 10 x 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} x^{3} d x - \int_{0}^{2} 2 x^{2} d x + \int_{0}^{2} 10 x d x

\int_{0}^{2} x^{3} d x = 4

\int_{0}^{2} 2 x^{2} d x = \frac{16}{3}

\int_{0}^{2} 10 x d x = 20

= 4 - \frac{16}{3} + 20

Simplify

4 - \frac{16}{3} + 20 : \frac{56}{3}

= \frac{56}{3}

What is the integral from 0 to 2 of x^3-2x^2+10x ?
The integral from 0 to 2 of x^3-2x^2+10x is 56/3