anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\int\limits4dy+3dx\]
anonymous
  • anonymous
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
anonymous
  • anonymous
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.

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anonymous
  • anonymous
Awesome, thank you!

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