find the integral of r(t) from 0 to 1

Question

find the integral of r(t)<t^4,2+t^2,3+t^2> from 0 to 1

anonymous · Answer

The result is a vector.  You just integrate each component separately.

queelius · Answer

As wio said, you just integrate each component separately. Specifically:

$$\int\limits_{0}^{1} r(t) dt = (\int\limits_{0}^{1} t^4 dt, \int\limits_{0}^{1} 2+t^2 dt, \int\limits_{0}^{1} 3+t^2 dt)$$

anonymous · Answer

so do u put plus c to each of them?

anonymous · Answer

at the end

queelius · Answer

Potentially, each C is a different constant, so make the C constant a vector constant, e.g., C = <c1, c2, c3>

anonymous · Answer

ohhh ughhhh i didnt put that on my exam :/ thanks tho! i just wanted to double check my answer

queelius · Answer

The constant of integration was a constant (hehe) thorn in my side while I was going through my school studies back in the day also. :)