Question

Evaluate ∫c〖sin⁡(x^3 )dx-xy +6dy〗 where c is the path starting at I, going by straight line to j then down to the origin, then back to i

Answer 1

this is a line integral

Answer 2

can you drow the pat, because it is not clear

Answer 3

draw the path**

Answer 4

:)

Answer 5

maybe this. But we need to know the values of i and j to have a numnerical solution

Answer 6

Yeah, but that is all there is to the question so I don't know how to solve it. No numericals were given for the i and j directions....

Answer 7

Are the i and j written as \(\vec{i}, \vec{j}\) (meaning the unit vectors), or are you supposed to assume they're general vectors with endpoints at \((x_1,y_1)\) and \((x_2,y_2)\), respectively?

Answer 8

In any case, you can write the vectors i and j as \((a,b)\) and \((c,d)\), then parameterize the paths. The triangle (as drawn by @myko) is given by the parameterization
\[C_1:\vec{r}(t)=(1-t)(a,b)+t(c,d),\; 0\le t\le1\\
C_2: \vec{r}(t)=(1-t)(c,d),\;0\le t\le1\\
C_3:\vec{r}(t)=t(a,b),\;0\le t\le1\]