What is the integral from-2 to 1 of (-5-2x^2)^2 ?

The integral from-2 to 1 of (-5-2x^2)^2 is 807/5

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integral from-2 to 1 of (-5-2x^2)^2

\int_{- 2}^{1} (- 5 - 2 x^{2})^{2} d x

\frac{807}{5}

Decimal Notation

161.4

Solution steps

\int_{- 2}^{1} (- 5 - 2 x^{2})^{2} d x

Factor

- 5 - 2 x^{2} : - (5 + 2 x^{2})

= \int_{- 2}^{1} (- (5 + 2 x^{2}))^{2} d x

Simplify

(- (5 + 2 x^{2}))^{2} : (5 + 2 x^{2})^{2}

= \int_{- 2}^{1} (5 + 2 x^{2})^{2} d x

Expand

(5 + 2 x^{2})^{2} : 25 + 20 x^{2} + 4 x^{4}

= \int_{- 2}^{1} 25 + 20 x^{2} + 4 x^{4} 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} 25 d x + \int_{- 2}^{1} 20 x^{2} d x + \int_{- 2}^{1} 4 x^{4} d x

\int_{- 2}^{1} 25 d x = 75

\int_{- 2}^{1} 20 x^{2} d x = 60

\int_{- 2}^{1} 4 x^{4} d x = \frac{132}{5}

= 75 + 60 + \frac{132}{5}

Simplify

75 + 60 + \frac{132}{5} : \frac{807}{5}

= \frac{807}{5}

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What is the integral from-2 to 1 of (-5-2x^2)^2 ?
The integral from-2 to 1 of (-5-2x^2)^2 is 807/5