What is integral from 0 to 1 of xf(x) ?

The answer to integral from 0 to 1 of xf(x) is f/3

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integral from 0 to 1 of xf(x)

\int_{0}^{1} x f (x) d x

\frac{f}{3}

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= f \cdot \int_{0}^{1} xx d x

Simplify

xx : x^{2}

= f \cdot \int_{0}^{1} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{1}

= f [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= f \frac{1}{3}

Simplify

= \frac{f}{3}

\frac{\partial}{\partial x} (2 x^{4} y - 3 x y + 9 y)

\frac{d y}{d x} = 3 x + y - 3

\int_{0}^{10} x e^{- 0.6 x} d x

\frac{\partial}{\partial y} (y (2 - x - y))

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

What is integral from 0 to 1 of xf(x) ?
The answer to integral from 0 to 1 of xf(x) is f/3