Question

what is vector integration? can you explain me by giving examples?

Answer 1

I think you mean integration of a vector function

Answer 2

its fairly straight forward, just like differentiation, it is done component wise

Answer 3

consider an example

r(t) = (3t +1)i + (5t^2 +cos(t))j + (4e^(2t))k = ((3t+1), (5t^2+cos(t)), (4e^(2t)))

Answer 4

integration is done component wise.

so the intgeral would be

( ( (3/2)t^2 +t ) , ( (5/3)t^3 +sin(t)) , 2e^(2t) ) +C

Answer 5

but C would be a constant VECTOR ( it has three components )

Answer 6

ok

Answer 7

thanks