What is the integral from 0 to 2 of (4ti-t^3j+5t^9k) ?

The integral from 0 to 2 of (4ti-t^3j+5t^9k) is 8i-j*4+512k

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integral from 0 to 2 of (4ti-t^3j+5t^9k)

\int_{0}^{2} (4 t i - t^{3} j + 5 t^{9} k) d t

8 i - j \cdot 4 + 512 k

Solution steps

\int_{0}^{2} 4 t i - t^{3} j + 5 t^{9} 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} 4 t i d t - \int_{0}^{2} t^{3} j d t + \int_{0}^{2} 5 t^{9} k d t

\int_{0}^{2} 4 t i d t = 8 i

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

\int_{0}^{2} 5 t^{9} k d t = 512 k

= 8 i - j \cdot 4 + 512 k

f (x) = coth (x)

1 - \frac{1}{x ^{2}}

x \to 0 lim (\frac{e ^{x}}{1 - e ^{x}})

\frac{\partial}{\partial x} (2 x^{2} - 4 x + 1)

\int (3 - 2 x)^{2} d x

What is the integral from 0 to 2 of (4ti-t^3j+5t^9k) ?
The integral from 0 to 2 of (4ti-t^3j+5t^9k) is 8i-j*4+512k