What is the integral from 1 to 10 of x^2(x-1) ?

The integral from 1 to 10 of x^2(x-1) is 8667/4

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integral from 1 to 10 of x^2(x-1)

\int_{1}^{10} x^{2} (x - 1) d x

\frac{8667}{4}

Decimal

2166.75

Solution steps

\int_{1}^{10} x^{2} (x - 1) d x

Expand

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

= \int_{1}^{10} 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}^{10} x^{3} d x - \int_{1}^{10} x^{2} d x

\int_{1}^{10} x^{3} d x = \frac{9999}{4}

\int_{1}^{10} x^{2} d x = 333

= \frac{9999}{4} - 333

Simplify

\frac{9999}{4} - 333 : \frac{8667}{4}

= \frac{8667}{4}

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\int_{2}^{4} (x + 2) d x

What is the integral from 1 to 10 of x^2(x-1) ?
The integral from 1 to 10 of x^2(x-1) is 8667/4