integral from-2 to 2 of x^2-y^2

解答

\int_{- 2}^{2} x^{2} - y^{2} d y

4 x^{2} - \frac{16}{3}

求解步骤

\int_{- 2}^{2} x^{2} - y^{2} d y

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 2}^{2} x^{2} d y - \int_{- 2}^{2} y^{2} d y

\int_{- 2}^{2} x^{2} d y = 4 x^{2}

\int_{- 2}^{2} y^{2} d y = \frac{16}{3}

= 4 x^{2} - \frac{16}{3}

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