Question

Let C be the curve which is the union of two line segments, the first going from (0, 0) to (4, -3) and the second going from (4, -3) to (8, 0).
Compute the line integral of int(4dy+3dx)

Answer 1

\[\int\limits4dy+3dx\]

Answer 2

This can done using Green's Theorem. The line integral over the boundary of the closed triangle
(0, 0) to (4, -3) to (8, 0) to (0,0) is equal to the double integral over area inside the triangle of the partial derivative of the partial derivative of 4 with respect to x -
the partial derivative of the partial derivative of 3 with respect to y = 0
See
http://mathworld.wolfram.com/GreensTheorem.html
Now the line integral can be divided into the three sides of the triangle
int_C1 + int_C2 + int_C3 = your integral + int_{8,0}^{0,0} on the x-axis=0
So
your integral =- int_{8,0}^{0,0} on the x-axis =int_0^8 3 dx= 24

You can practice online calculus problems on
http://moltest.missouri.edu/mucgi-bin/calculus.cgi

Answer 3

Of course, you can do it by parametrizing the two line and use the definition of the line integral, but the first method is shorter.

Answer 4

Awesome, thank you!