What is the integral from 0 to 2 of (ti-t^3j+3t^5k) ?

The integral from 0 to 2 of (ti-t^3j+3t^5k) is i2-j*4+32k

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integral from 0 to 2 of (ti-t^3j+3t^5k)

\int_{0}^{2} (t i - t^{3} j + 3 t^{5} k) d t

i 2 - j \cdot 4 + 32 k

Solution steps

\int_{0}^{2} t i - t^{3} j + 3 t^{5} k d t

Apply the Sum Rule:

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

= \int_{0}^{2} t i d t - \int_{0}^{2} t^{3} j d t + \int_{0}^{2} 3 t^{5} k d t

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

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

\int_{0}^{2} 3 t^{5} k d t = 32 k

= i 2 - j \cdot 4 + 32 k

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What is the integral from 0 to 2 of (ti-t^3j+3t^5k) ?
The integral from 0 to 2 of (ti-t^3j+3t^5k) is i2-j*4+32k