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Popular Calculus >

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

Solution

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

Solution

\frac{10}{3}

+1

Decimal

3.33333 \dots

Solution steps

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

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

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

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

= 2 - \frac{8}{3} + 4

Simplify

2 - \frac{8}{3} + 4 : \frac{10}{3}

= \frac{10}{3}

Graph

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Frequently Asked Questions (FAQ)

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