What is the integral from 0 to 1 of x^4-2x^3+x^2 ?

The integral from 0 to 1 of x^4-2x^3+x^2 is 1/30

integral from 0 to 1 of x^4-2x^3+x^2

\int_{0}^{1} x^{4} - 2 x^{3} + x^{2} d x

\frac{1}{30}

Decimal

0.03333 \dots

Solution steps

\int_{0}^{1} x^{4} - 2 x^{3} + 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^{4} d x - \int_{0}^{1} 2 x^{3} d x + \int_{0}^{1} x^{2} d x

\int_{0}^{1} x^{4} d x = \frac{1}{5}

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

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

= \frac{1}{5} - \frac{1}{2} + \frac{1}{3}

Simplify

\frac{1}{5} - \frac{1}{2} + \frac{1}{3} : \frac{1}{30}

= \frac{1}{30}

\frac{\partial}{\partial x} (9 - 2 x^{2} + 3 y^{2})

\frac{\partial}{\partial x} (cos (2 x + 5 y) \cdot 5)

d er i v a t i v e - 15 ln (x)

\int_{0}^{1} e^{- 4 x^{2}} d x

y^{^{'}} = 0.0016 y (2500 - y)

What is the integral from 0 to 1 of x^4-2x^3+x^2 ?
The integral from 0 to 1 of x^4-2x^3+x^2 is 1/30