What is the integral from-3 to-1 of (y^5-2y)/(y^3) ?

The integral from-3 to-1 of (y^5-2y)/(y^3) is 22/3

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integral from-3 to-1 of (y^5-2y)/(y^3)

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

\frac{22}{3}

Decimal

7.33333 \dots

Solution steps

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

Expand

\frac{y ^{5} - 2 y}{y ^{3}} : y^{2} - \frac{2}{y ^{2}}

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

\int_{- 3}^{- 1} y^{2} d y = \frac{26}{3}

\int_{- 3}^{- 1} \frac{2}{y ^{2}} d y = \frac{4}{3}

= \frac{26}{3} - \frac{4}{3}

Simplify

\frac{26}{3} - \frac{4}{3} : \frac{22}{3}

= \frac{22}{3}

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What is the integral from-3 to-1 of (y^5-2y)/(y^3) ?
The integral from-3 to-1 of (y^5-2y)/(y^3) is 22/3