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

The integral from 1 to 3/2 of 3y-2y^2 is 7/24

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integral from 1 to 3/2 of 3y-2y^2

\int_{1}^{\frac{3}{2}} 3 y - 2 y^{2} d y

\frac{7}{24}

Decimal Notation

0.29166 \dots

Solution steps

\int_{1}^{\frac{3}{2}} 3 y - 2 y^{2} d y

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}^{\frac{3}{2}} 3 y d y - \int_{1}^{\frac{3}{2}} 2 y^{2} d y

\int_{1}^{\frac{3}{2}} 3 y d y = \frac{15}{8}

\int_{1}^{\frac{3}{2}} 2 y^{2} d y = \frac{19}{12}

= \frac{15}{8} - \frac{19}{12}

Simplify

\frac{15}{8} - \frac{19}{12} : \frac{7}{24}

= \frac{7}{24}

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What is the integral from 1 to 3/2 of 3y-2y^2 ?
The integral from 1 to 3/2 of 3y-2y^2 is 7/24