integral from 0 to pi of (3x^2-sin(x)+2)

解答

\int_{0}^{π} (3 x^{2} - sin (x) + 2) d x

π^{3} - 2 + 2 π

十进制

35.28946 \dots

求解步骤

\int_{0}^{π} 3 x^{2} - sin (x) + 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}^{π} 3 x^{2} d x - \int_{0}^{π} sin (x) d x + \int_{0}^{π} 2 d x

\int_{0}^{π} 3 x^{2} d x = π^{3}

\int_{0}^{π} sin (x) d x = 2

\int_{0}^{π} 2 d x = 2 π

= π^{3} - 2 + 2 π

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