- We are asked to evaluate the given line integral where C consists of line segments from (0,0) to (9,1) and from (9,1) to (10,0)
First i parametrized the given line segments and divided the curve C as two curves
Now that i have defined the path in terms of a parameter, i will use the following equation to evaluate our line integral where x’(t) and y’(t) are the derivatives of the components of the parametrized line segments
First, we will integrate over the first line segment < 9t , t > from t=0 to t=1. x’(t)=9 and y’(t)=1
Now we integrate over our second line segment < 9+t , 1-t > from t=0 to t=1. here x’(t)=1 and y’(t)=-1
Finally we add up the results of both line integrals
However this is the wrong answer. Is the mistake algebraic or conceptual? Im not sure where i went wrong