What is the integral from 0 to 2 of (8ti-t^3j+2t^3k) ?

The integral from 0 to 2 of (8ti-t^3j+2t^3k) is 16i-j*4+8k

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

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

16 i - j \cdot 4 + 8 k

Solution steps

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

= 16 i - j \cdot 4 + 8 k

\int_{0}^{\frac{π}{6}} tan (3 x) d x

n = 1 \sum \infty \frac{ln ( n )}{n !}

\frac{d}{d x} (\frac{x}{1 + x})

\int 4 e^{- \frac{x}{4}} d x

f (x) = - 2 sin (x)

What is the integral from 0 to 2 of (8ti-t^3j+2t^3k) ?
The integral from 0 to 2 of (8ti-t^3j+2t^3k) is 16i-j*4+8k