What is the integral from 0 to 1 of xsin(2)x^2 ?

The integral from 0 to 1 of xsin(2)x^2 is sin(2) 1/4

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integral from 0 to 1 of xsin(2)x^2

\int_{0}^{1} x sin (2) x^{2} d x

sin (2) \frac{1}{4}

Decimal Notation

0.22732 \dots

Solution steps

\int_{0}^{1} x sin (2) x^{2} d x

Take the constant out:

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

= sin (2) \cdot \int_{0}^{1} x x^{2} d x

Simplify

x x^{2} : x^{3}

= sin (2) \cdot \int_{0}^{1} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{0}^{1}

= sin (2) [\frac{x ^{4}}{4}]_{0}^{1}

Compute the boundaries:

\frac{1}{4}

= sin (2) \frac{1}{4}

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What is the integral from 0 to 1 of xsin(2)x^2 ?
The integral from 0 to 1 of xsin(2)x^2 is sin(2) 1/4