What is the integral from 0 to 5/3 of 3x^2-5x ?

The integral from 0 to 5/3 of 3x^2-5x is -125/54

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integral from 0 to 5/3 of 3x^2-5x

\int_{0}^{\frac{5}{3}} 3 x^{2} - 5 x d x

- \frac{125}{54}

Decimal Notation

- 2.31481 \dots

Solution steps

\int_{0}^{\frac{5}{3}} 3 x^{2} - 5 x 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}^{\frac{5}{3}} 3 x^{2} d x - \int_{0}^{\frac{5}{3}} 5 x d x

\int_{0}^{\frac{5}{3}} 3 x^{2} d x = \frac{125}{27}

\int_{0}^{\frac{5}{3}} 5 x d x = \frac{125}{18}

= \frac{125}{27} - \frac{125}{18}

Simplify

\frac{125}{27} - \frac{125}{18} : - \frac{125}{54}

= - \frac{125}{54}

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What is the integral from 0 to 5/3 of 3x^2-5x ?
The integral from 0 to 5/3 of 3x^2-5x is -125/54