integral from 0 to 4 of 5x^2+3x+1

解答

\int_{0}^{4} 5 x^{2} + 3 x + 1 d x

\frac{404}{3}

十进制

134.66666 \dots

求解步骤

\int_{0}^{4} 5 x^{2} + 3 x + 1 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}^{4} 5 x^{2} d x + \int_{0}^{4} 3 x d x + \int_{0}^{4} 1 d x

\int_{0}^{4} 5 x^{2} d x = \frac{320}{3}

\int_{0}^{4} 3 x d x = 24

\int_{0}^{4} 1 d x = 4

= \frac{320}{3} + 24 + 4

化简

\frac{320}{3} + 24 + 4 : \frac{404}{3}

= \frac{404}{3}

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