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

The integral from-1 to 2 of x^2(3-2x) is 3/2

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integral from-1 to 2 of x^2(3-2x)

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

\frac{3}{2}

Decimal Notation

1.5

Solution steps

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

Apply Integration By Parts

: [\frac{1}{3} x^{3} (3 - 2 x) - \int - \frac{2 x ^{3}}{3} d x]_{- 1}^{2}

= [\frac{1}{3} x^{3} (3 - 2 x) - \int - \frac{2 x ^{3}}{3} d x]_{- 1}^{2}

\int - \frac{2 x ^{3}}{3} d x = - \frac{x ^{4}}{6}

= [\frac{1}{3} x^{3} (3 - 2 x) - (- \frac{x ^{4}}{6})]_{- 1}^{2}

Simplify

[\frac{1}{3} x^{3} (3 - 2 x) - (- \frac{x ^{4}}{6})]_{- 1}^{2} : [\frac{1}{2} x^{3} (- x + 2)]_{- 1}^{2}

= [\frac{1}{2} x^{3} (- x + 2)]_{- 1}^{2}

Compute the boundaries:

\frac{3}{2}

= \frac{3}{2}

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