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Popular >

integral from 0 to 1 of x-x^2

Solution

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

Solution

\frac{1}{6}

+1

Decimal Notation

0.16666 \dots

Solution steps

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

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

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= \frac{1}{2} - \frac{1}{3}

Simplify

\frac{1}{2} - \frac{1}{3} : \frac{1}{6}

= \frac{1}{6}

Popular Examples

area y=x^2+2x+1,y=2x+5 area

y = x^{2} + 2 x + 1, y = 2 x + 5

(\partial)/(\partial x)(-6xy)

\frac{\partial}{\partial x} (- 6 x y)

derivative of 1/5 x^5+1/(12x^3)

\frac{d}{d x} (\frac{1}{5} x^{5} + \frac{1}{12 x ^{3}})

x^2y^'-2xy=sin(4x)x^4

x^{2} y^{^{'}} - 2 x y = sin (4 x) x^{4}

maclaurin arctan(3x)maclaurin

arctan (3 x)

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x-x^2 ?
The integral from 0 to 1 of x-x^2 is 1/6