What is integral from 1 to 4 of xf(x) ?

The answer to integral from 1 to 4 of xf(x) is f*21

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integral from 1 to 4 of xf(x)

\int_{1}^{4} x f (x) d x

f \cdot 21

Solution steps

\int_{1}^{4} 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_{1}^{4} xx d x

Simplify

xx : x^{2}

= f \cdot \int_{1}^{4} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{1}^{4}

= f [\frac{x ^{3}}{3}]_{1}^{4}

Compute the boundaries:

21

= f \cdot 21

\int \frac{x ^{2} + 4}{x ^{2}} d x

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

\int \frac{x - 1}{x + 1} d x

e^{- x}

5 cos (π x)

What is integral from 1 to 4 of xf(x) ?
The answer to integral from 1 to 4 of xf(x) is f*21