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

Popular >

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

\int_{1}^{3} x^{2} - x - 2 d x

\int_{0}^{3} 2 π (10 - x) (2 x) d x

\int_{0}^{2 π} \frac{1 - cos ( 2 θ )}{2} d θ

\int_{0}^{x} 0.5 x d x

\int_{- 64}^{125} \frac{1}{x ^{\frac{1}{3}}} d x

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