What is the integral from-4 to-2 of (y^2+1/(y^3)) ?

The integral from-4 to-2 of (y^2+1/(y^3)) is 1783/96

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integral from-4 to-2 of (y^2+1/(y^3))

\int_{- 4}^{- 2} (y^{2} + \frac{1}{y ^{3}}) d y

\frac{1783}{96}

Decimal

18.57291 \dots

Solution steps

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

\int_{- 4}^{- 2} y^{2} d y = \frac{56}{3}

\int_{- 4}^{- 2} \frac{1}{y ^{3}} d y = - \frac{3}{32}

= \frac{56}{3} - \frac{3}{32}

Simplify

\frac{56}{3} - \frac{3}{32} : \frac{1783}{96}

= \frac{1783}{96}

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What is the integral from-4 to-2 of (y^2+1/(y^3)) ?
The integral from-4 to-2 of (y^2+1/(y^3)) is 1783/96