integral from x^2 to sqrt(x of)xy

解答

\int_{x^{2}}^{x} x y d y

\frac{x ( x - x ^{4} )}{2}

求解步骤

\int_{x^{2}}^{x} x y d y

提出常数:

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

= x \cdot \int_{x^{2}}^{x} y d y

使用幂法则

= x [\frac{y ^{2}}{2}]_{x^{2}}^{x}

带入上下限计算后得:

\frac{x}{2} - \frac{x ^{4}}{2}

= x (\frac{x}{2} - \frac{x ^{4}}{2})

化简

= \frac{x ( x - x ^{4} )}{2}

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