What is the integral from 0 to 2 of 4xsin(n)x ?

The integral from 0 to 2 of 4xsin(n)x is 32/3 sin(n)

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integral from 0 to 2 of 4xsin(n)x

\int_{0}^{2} 4 x sin (n) x d x

\frac{32}{3} sin (n)

Solution steps

\int_{0}^{2} 4 x sin (n) x d x

Take the constant out:

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

= 4 sin (n) \cdot \int_{0}^{2} xx d x

Simplify

xx : x^{2}

= 4 sin (n) \cdot \int_{0}^{2} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{2}

= 4 sin (n) [\frac{x ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= 4 sin (n) \frac{8}{3}

Simplify

= \frac{32}{3} sin (n)

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What is the integral from 0 to 2 of 4xsin(n)x ?
The integral from 0 to 2 of 4xsin(n)x is 32/3 sin(n)