Calculate the line integral
$\displaystyle \int$_{c }F dr
where c is given by r(t) = < t, t^2, t^3> , 0<= t <= 1
and F(x,y,z) = (sin(y) - y^2sin(x) , xcosy + 2ycosx , 1)
really not sure how to get started on this. any help would be great
Calculate the line integral
$\displaystyle \int$_{c }F dr
where c is given by r(t) = < t, t^2, t^3> , 0<= t <= 1
and F(x,y,z) = (sin(y) - y^2sin(x) , xcosy + 2ycosx , 1)
really not sure how to get started on this. any help would be great
It's really just straightforward calculation. r(t) = < t, t^2, t^3> so dr= <1, 2t, 3t^2> dt.
F(x,y,z) = <sin(y) - y^2sin(x) , xcosy + 2ycosx , 1> so F dr= (sin(y)- y^2sin(x))+ 2t(xcos(y)- 2ycos(x))+ 3t^2)dt
Now replace x and y in that by t and t^2, respectively. Then integrate from t= 0 to t= 1.