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A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration of (x + y)2 on path AB traversed in a counter clockwise sense is
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π - 1 2
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π + 1 2
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π 2
- 1
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Correct Option: B
Given :x2 + y2 = 1
Put x = cos θ, and y = sin θ
(x + y)2 = cos2θ+ sin2θ + 2 sinθ cosθ
= 1 + sin 2θ
| = |  | (1 + sin2θ) dθ |
| = |  | θ - |  | π / 2 | = | | + | + | | ||||
| 2 | 0 | 2 | 2 | 2 |
| = |  | + 1 |  | |
| 2 |
