What is the integral from 0 to 1 of 1-x^{2/5} ?

The integral from 0 to 1 of 1-x^{2/5} is 2/7

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integral from 0 to 1 of 1-x^{2/5}

\int_{0}^{1} 1 - x^{\frac{2}{5}} d x

\frac{2}{7}

Decimal Notation

0.28571 \dots

Solution steps

\int_{0}^{1} 1 - x^{\frac{2}{5}} 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} 1 d x - \int_{0}^{1} x^{\frac{2}{5}} d x

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

\int_{0}^{1} x^{\frac{2}{5}} d x = \frac{5}{7}

= 1 - \frac{5}{7}

Simplify

1 - \frac{5}{7} : \frac{2}{7}

= \frac{2}{7}

f (x) = x^{3} - x^{2} - x, g (x) = x

(2 x y^{3} - 3 x^{2} y^{2}) d x + (x y^{3} + 2 x^{2} y^{2}) d y = 0

\frac{d y}{d t} = 0.04 y (400 - y)

\int x - 1 d x

\int \frac{1}{( ( x - 1 ) ( x ^{2} + 1 ) )} d x

What is the integral from 0 to 1 of 1-x^{2/5} ?
The integral from 0 to 1 of 1-x^{2/5} is 2/7