I am currently doing this question from a book and I seem to be getting different answeres than the ones specified. Question
My current working is as follows $$ \vec F=(2t^3+3)\vec i+2t^5\vec j+(t^4-2t^2)\vec k $$ $$ \vec r=2t^2\vec i+t\vec j+t^3\vec k $$
$$ dr =4t+1+3t^2 dt $$
$$ \int_C\vec F.dr = \int_0^1(2t^3+3)(4t)+2t^5+(t^4-2t^2)3t^2 dt = \frac{752}{105} =7.162 $$ while the answer from the book says 288/35 approx 8.229 Can you help me pinpoint where I went wrong?
$$ \vec F=(2t+3)\vec i+2t^5\vec j+(t^4-2t^2)\vec k$$
$$ \int_C\vec F.dr = \int_0^1(2t+3)(4t)+2t^5+(t^4-2t^2)3t^2 dt = \frac{288}{35}$$