What is the integral from 0 to 2 of (6ti-t^3j+5t^9k) ?

The integral from 0 to 2 of (6ti-t^3j+5t^9k) is 12i-j*4+512k

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integral from 0 to 2 of (6ti-t^3j+5t^9k)

\int_{0}^{2} (6 t i - t^{3} j + 5 t^{9} k) d t

12 i - j \cdot 4 + 512 k

Solution steps

\int_{0}^{2} 6 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} 6 t i d t - \int_{0}^{2} t^{3} j d t + \int_{0}^{2} 5 t^{9} k d t

\int_{0}^{2} 6 t i d t = 12 i

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

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

= 12 i - j \cdot 4 + 512 k

x \to 0 lim (\frac{x + 5}{3 x})

\frac{\partial}{\partial x} ((e^{\frac{x}{2}}) (2 x y))

\frac{x ^{2}}{x - 9}

x^{\frac{1}{3}}

(a - 7 x) (a + 7 x)

What is the integral from 0 to 2 of (6ti-t^3j+5t^9k) ?
The integral from 0 to 2 of (6ti-t^3j+5t^9k) is 12i-j*4+512k