What is the integral from 1 to 5 of 5x^2-x/3 ?

The integral from 1 to 5 of 5x^2-x/3 is 608/3

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integral from 1 to 5 of 5x^2-x/3

\int_{1}^{5} 5 x^{2} - \frac{x}{3} d x

\frac{608}{3}

Decimal

202.66666 \dots

Solution steps

\int_{1}^{5} 5 x^{2} - \frac{x}{3} 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}^{5} 5 x^{2} d x - \int_{1}^{5} \frac{x}{3} d x

\int_{1}^{5} 5 x^{2} d x = \frac{620}{3}

\int_{1}^{5} \frac{x}{3} d x = 4

= \frac{620}{3} - 4

Simplify

\frac{620}{3} - 4 : \frac{608}{3}

= \frac{608}{3}

What is the integral from 1 to 5 of 5x^2-x/3 ?
The integral from 1 to 5 of 5x^2-x/3 is 608/3