integral from 4 to x of (64)/(t^5)

解答

\int_{4}^{x} \frac{64}{t ^{5}} d t

64 (- \frac{1}{4 x ^{4}} + \frac{1}{1024})

求解步骤

\int_{4}^{x} \frac{64}{t ^{5}} d t

提出常数:

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

= 64 \cdot \int_{4}^{x} \frac{1}{t ^{5}} d t

使用幂法则

= 64 [- \frac{1}{4 t ^{4}}]_{4}^{x}

带入上下限计算后得:

- \frac{1}{4 x ^{4}} + \frac{1}{1024}

= 64 (- \frac{1}{4 x ^{4}} + \frac{1}{1024})