integral from 0 to 2 of (8ti-t^3j+4t^7k)

解答

\int_{0}^{2} (8 t i - t^{3} j + 4 t^{7} k) d t

16 i - j \cdot 4 + 128 k

求解步骤

\int_{0}^{2} 8 t i - t^{3} j + 4 t^{7} k d t

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{2} 8 t i d t - \int_{0}^{2} t^{3} j d t + \int_{0}^{2} 4 t^{7} k d t

\int_{0}^{2} 8 t i d t = 16 i

\int_{0}^{2} t^{3} j d t = j \cdot 4

\int_{0}^{2} 4 t^{7} k d t = 128 k

= 16 i - j \cdot 4 + 128 k

x \to 3 - lim (6 - x)

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\int cot^{5} (\frac{x}{2}) csc^{2} (\frac{x}{2}) d x

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\int \frac{3}{sec ( x ) - 1} d x