c-3xy-e-sin-x-dx-7x-y-4-1-dy-C-triangle-with-vertex-0-0-0-1-and-1-0-

Question Number 117493 by bobhans last updated on 12/Oct/20

\int_{c} (3 xy - e^{\sin x}) dx + (7 x + \sqrt{y^{4} + 1}) dy

C : triangle with vertex (0, 0), (0, 1)

and (1, 0)

Answered by bemath last updated on 12/Oct/20

Green Theorem

\int_{c} Pdx + Qdy = \int \int_{D} (Q_{x} - P_{y}) dxdy

= \int \int_{D} (7 - 3 x) dxdy

= \underset{0}{\int^{1}} \underset{0}{\int^{1 - x}} (7 - 3 x) dydx

= \underset{0}{\int^{1}} (7 - 3 x) (1 - x) dx

= {\int^{1}}_{0} (7 - 10 x + {3 x}^{2}) dx

= {[7 x - {5 x}^{2} + x^{3}]}_{0}^{1} = 3

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