What is the integral from 0 to 1 of (x^3-x^2+1) ?

The integral from 0 to 1 of (x^3-x^2+1) is 11/12

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integral from 0 to 1 of (x^3-x^2+1)

\int_{0}^{1} (x^{3} - x^{2} + 1) d x

\frac{11}{12}

Decimal

0.91666 \dots

Solution steps

\int_{0}^{1} x^{3} - x^{2} + 1 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_{0}^{1} x^{3} d x - \int_{0}^{1} x^{2} d x + \int_{0}^{1} 1 d x

\int_{0}^{1} x^{3} d x = \frac{1}{4}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} 1 d x = 1

= \frac{1}{4} - \frac{1}{3} + 1

Simplify

\frac{1}{4} - \frac{1}{3} + 1 : \frac{11}{12}

= \frac{11}{12}

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What is the integral from 0 to 1 of (x^3-x^2+1) ?
The integral from 0 to 1 of (x^3-x^2+1) is 11/12