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Popular >

integral from 0 to 2 of x-x^2

Solution

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

Solution

- \frac{2}{3}

+1

Decimal Notation

- 0.66666 \dots

Solution steps

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

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

= 2 - \frac{8}{3}

Simplify

2 - \frac{8}{3} : - \frac{2}{3}

= - \frac{2}{3}

Popular Examples

integral of sin^5(θ)cos(θ)

\int sin^{5} (θ) cos (θ) d θ

tangent of x^2y^2=16,(1,4)tangent of

x^{2} y^{2} = 16, (1, 4)

(\partial)/(\partial x)(5-3x^2-y^2)

\frac{\partial}{\partial x} (5 - 3 x^{2} - y^{2})

(dy)/(dx)-x^2y=0

\frac{d y}{d x} - x^{2} y = 0

integral of x^7[0.7]

\int x^{7} [0.7] d x

Frequently Asked Questions (FAQ)

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