integral from 1 to 3 of sqrt(x^2+x^4)

解答

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

\frac{10 10 - 2 2}{3}

十进制

9.59811 \dots

求解步骤

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

化简

x^{2} + x^{4} : x^{2} 1 + x^{2}

= \int_{1}^{3} x^{2} 1 + x^{2} d x

x^{2} = (x),

假定

x \geq 0

= \int_{1}^{3} x 1 + x^{2} d x

使用换元积分法

= \int_{2}^{10} u^{2} d u

使用幂法则

= [\frac{u ^{3}}{3}]_{2}^{10}

带入上下限计算后得:

\frac{10 10 - 2 2}{3}

= \frac{10 10 - 2 2}{3}

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