∫((e^-t)<3,t,sin(t)>dt)?
∫(<3(e^-t),t(e^-t),(e^-t)sin(t)>dt
so
it equals
-3e^-t i + (-t-1)e^-t j + (e^-t)((-cos(t)-sin(t))/2)k + C
? right?
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∫(<3(e^-t),t(e^-t),(e^-t)sin(t)>dt
so
it equals
-3e^-t i + (-t-1)e^-t j + (e^-t)((-cos(t)-sin(t))/2)k + C
? right?
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Verified answer
yes, your solution is correct.
the vector <X,Y,Z> is also: Xi + Yj + Zk and since the integral of a sum is the sum of the integral you do what you did, integrate 3 different things, one for each vector coordinate.
WRONG