integral from 0 to a of 1-(x^2)/(a^2)

解答

\int_{0}^{a} 1 - \frac{x ^{2}}{a ^{2}} d x

a - \frac{a}{3}

求解步骤

\int_{0}^{a} 1 - \frac{x ^{2}}{a ^{2}} d x

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_{0}^{a} 1 d x - \int_{0}^{a} \frac{x ^{2}}{a ^{2}} d x

\int_{0}^{a} 1 d x = a

\int_{0}^{a} \frac{x ^{2}}{a ^{2}} d x = \frac{a}{3}

= a - \frac{a}{3}

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