What is the integral from 0 to 2 of (4ti-t^3j+4t^7k) ?

The integral from 0 to 2 of (4ti-t^3j+4t^7k) is 8i-j*4+128k

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

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

8 i - j \cdot 4 + 128 k

Solution steps

\int_{0}^{2} 4 t i - t^{3} j + 4 t^{7} 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} 4 t^{7} 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} 4 t^{7} k d t = 128 k

= 8 i - j \cdot 4 + 128 k

y = x^{4} + 2 x^{2} - x

x \to 2 lim (2 x^{3})

\frac{d}{d x} (- x^{- 3})

\int - \frac{x + 1}{x} d x

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0

What is the integral from 0 to 2 of (4ti-t^3j+4t^7k) ?
The integral from 0 to 2 of (4ti-t^3j+4t^7k) is 8i-j*4+128k