integral from x-3 to x+3 of 2/393 y

解答

\int_{x - 3}^{x + 3} \frac{2}{393} y d y

\frac{4 x}{131}

求解步骤

\int_{x - 3}^{x + 3} \frac{2}{393} y d y

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{393} \cdot \int_{x - 3}^{x + 3} y d y

使用幂法则

= \frac{2}{393} [\frac{y ^{2}}{2}]_{x - 3}^{x + 3}

带入上下限计算后得:

\frac{( x + 3 ) ^{2}}{2} - \frac{( x - 3 ) ^{2}}{2}

= \frac{2}{393} (\frac{( x + 3 ) ^{2}}{2} - \frac{( x - 3 ) ^{2}}{2})

化简

= \frac{4 x}{131}

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