What is the integral from 0 to 7/2 of 7x-2x^2 ?

The integral from 0 to 7/2 of 7x-2x^2 is 343/24

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integral from 0 to 7/2 of 7x-2x^2

\int_{0}^{\frac{7}{2}} 7 x - 2 x^{2} d x

\frac{343}{24}

Decimal

14.29166 \dots

Solution steps

\int_{0}^{\frac{7}{2}} 7 x - 2 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_{0}^{\frac{7}{2}} 7 x d x - \int_{0}^{\frac{7}{2}} 2 x^{2} d x

\int_{0}^{\frac{7}{2}} 7 x d x = \frac{343}{8}

\int_{0}^{\frac{7}{2}} 2 x^{2} d x = \frac{343}{12}

= \frac{343}{8} - \frac{343}{12}

Simplify

\frac{343}{8} - \frac{343}{12} : \frac{343}{24}

= \frac{343}{24}

What is the integral from 0 to 7/2 of 7x-2x^2 ?
The integral from 0 to 7/2 of 7x-2x^2 is 343/24