Question

calc 3 help

evaluate the line integral (y-x)dx+xydy along the line segment from (3,4) to (2,1)

Answer 1

Well find the equation of the line from (3,4) to (2,1). We do not need an extra parameter in this case, we may simply write it in terms of x:
y=3x-5.
And so:
dy=3dx.
Now we are integrating along the above line from x=2 to x=3. Plug all of this in:
\[\int\limits_{2}^{3}[(3x-5-x)+x(3x-5)(3)]dx=\int\limits_{2}^{3}(9x^2-13x-5)dx=\left [3x^3-\frac{13}{2}x^2-5x\right ]_2^3\]Which is equal to 39.