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Question

F(x,y) = (x2+xy) ^ax + (y2+xy) ^ay. It's line integral over the straight line from (x,y) = (0,2) to (2,0) evaluates to

A
-8
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B
4
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C
8
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D
0
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Solution

The correct option is D 0
Equation of straight line
x2+y2 = 1
x + y =2
Now, dl = dx^ax+dy^ay
and F=(x2+xy)^ax+(y2+xy)^ay

Line integral of F (x,y)

LF(x,y).dl=L(x2+xy)dx+((y2+xy)dy
=20(x2+x(2x))dx+20(y2+(2y)y)dy
=[x2]20+[y2]02
=4 - 0 + 0 - 4 = 0

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