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

The integral from-2 to-1 of (2x^3+1/(x^2)) is -7

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

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

- 7

Solution steps

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

\int_{- 2}^{- 1} 2 x^{3} d x = - \frac{15}{2}

\int_{- 2}^{- 1} \frac{1}{x ^{2}} d x = \frac{1}{2}

= - \frac{15}{2} + \frac{1}{2}

Simplify

- \frac{15}{2} + \frac{1}{2} : - 7

= - 7

\int_{- 1}^{1} (2 - x^{2} - x^{2}) d x

\int_{0}^{2} \frac{1}{x ^{4}} d x

\int_{1}^{4} 5 x^{4} d x

\int_{0}^{1} (\frac{x + 5}{2})^{2} d x

\int_{1}^{3} x^{3} + x + 6 d x

What is the integral from-2 to-1 of (2x^3+1/(x^2)) ?
The integral from-2 to-1 of (2x^3+1/(x^2)) is -7