integral from-x to x of x^3y^2

解答

\int_{- x}^{x} x^{3} y^{2} d y

\frac{2 x ^{6}}{3}

求解步骤

\int_{- x}^{x} x^{3} y^{2} d y

提出常数:

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

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

使用幂法则

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

带入上下限计算后得:

2 \cdot \frac{x ^{3}}{3}

= x^{3} \cdot 2 \cdot \frac{x ^{3}}{3}

化简

= \frac{2 x ^{6}}{3}

\int_{0}^{x} (x - t) d t

\int_{0}^{π} (8 + sin (x)) d x

\int_{1}^{2} sin (π t) d t

\int_{1}^{\infty} \frac{5}{x ^{2} + 4} d x

\int_{- 2}^{8} (8 x + 6) d x