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

The integral from-1 to 2 of (x+2)^2-(x^2)^2 is 72/5

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

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

\frac{72}{5}

Decimal

14.4

Solution steps

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

(x^{2})^{2} = x^{4}

= \int_{- 1}^{2} (x + 2)^{2} - 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_{- 1}^{2} (x + 2)^{2} d x - \int_{- 1}^{2} x^{4} d x

\int_{- 1}^{2} (x + 2)^{2} d x = 21

\int_{- 1}^{2} x^{4} d x = \frac{33}{5}

= 21 - \frac{33}{5}

Simplify

21 - \frac{33}{5} : \frac{72}{5}

= \frac{72}{5}

What is the integral from-1 to 2 of (x+2)^2-(x^2)^2 ?
The integral from-1 to 2 of (x+2)^2-(x^2)^2 is 72/5