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The value of ∫[(3x - 8y²)dx (4y - 6xy) dy] (where C is the boundary of the region boundary by x = 0, y = 0 and x + y = 1) is ________.
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- 1.524
- 3.66
- 1.666
- 2.65
Correct Option: B
∫c[(3x - 8y²)dx + (4y - 6xy)dy],
C is boundary of region bounded by x = 0, y =1, and z + y = 1
By using Green's theoren, we get
| I = ∮c(pdx + Qdy) dx = ∮R∮ |  |  | dx dy | ||
| δv | δy |
Her P = 3x – 8y²
Q = 4y – 6xy
| = -6y | ||
| δx |
| = -16y | ||
| δx |
I = ∫∫(-6y -(16y)dx dy
I = ∫∫ 10y dx dy
| I = 101∫0dx1-x∫0 | ||
| 2 |
I = 51∫0dx(1 - x)²
I = 1.666
