What is the integral from 1 to 2 of x(3/7 x^2) ?

The integral from 1 to 2 of x(3/7 x^2) is 45/28

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integral from 1 to 2 of x(3/7 x^2)

\int_{1}^{2} x (\frac{3}{7} x^{2}) d x

\frac{45}{28}

Decimal Notation

1.60714 \dots

Solution steps

\int_{1}^{2} x \frac{3}{7} x^{2} d x

Take the constant out:

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

= \frac{3}{7} \cdot \int_{1}^{2} x x^{2} d x

Simplify

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

= \frac{3}{7} \cdot \int_{1}^{2} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{1}^{2}

= \frac{3}{7} [\frac{x ^{4}}{4}]_{1}^{2}

Compute the boundaries:

\frac{15}{4}

= \frac{3}{7} \cdot \frac{15}{4}

Simplify

= \frac{45}{28}

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What is the integral from 1 to 2 of x(3/7 x^2) ?
The integral from 1 to 2 of x(3/7 x^2) is 45/28