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

The integral from 0 to 2 of (x^2+3x-3) is 8/3

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integral from 0 to 2 of (x^2+3x-3)

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

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 3 x d x = 6

\int_{0}^{2} 3 d x = 6

= \frac{8}{3} + 6 - 6

Simplify

= \frac{8}{3}

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

\int_{2}^{8} 8 d x

\int_{\frac{1}{2}}^{1} 3 x d x

\int_{0}^{π} (sin (x) + cos (x)) d x

\int_{0}^{1} 12 x d x

What is the integral from 0 to 2 of (x^2+3x-3) ?
The integral from 0 to 2 of (x^2+3x-3) is 8/3