What is the integral from 1 to 6 of x^2(x-1) ?

The integral from 1 to 6 of x^2(x-1) is 3025/12

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integral from 1 to 6 of x^2(x-1)

\int_{1}^{6} x^{2} (x - 1) d x

\frac{3025}{12}

Decimal

252.08333 \dots

Solution steps

\int_{1}^{6} x^{2} (x - 1) d x

Expand

x^{2} (x - 1) : x^{3} - x^{2}

= \int_{1}^{6} x^{3} - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{6} x^{3} d x - \int_{1}^{6} x^{2} d x

\int_{1}^{6} x^{3} d x = \frac{1295}{4}

\int_{1}^{6} x^{2} d x = \frac{215}{3}

= \frac{1295}{4} - \frac{215}{3}

Simplify

\frac{1295}{4} - \frac{215}{3} : \frac{3025}{12}

= \frac{3025}{12}

\int_{a}^{b} (x) d x

\int_{- 6}^{1} 2 x + 6 d x

\int_{0}^{\infty} e^{- 2 y} d y

\int_{4}^{9} x d x

\int_{- 2}^{1} - x^{2} + 5 d x

What is the integral from 1 to 6 of x^2(x-1) ?
The integral from 1 to 6 of x^2(x-1) is 3025/12