Verify Green's Theorem by evaluating both integrals |y? dx + x2 dy = Ne dA ду for the given path. C: boundary of the region lying between the graphs of y = x and y = Vx 11 2 dx + x² dy = 30 L/-) an - - 30 ON OM 11 dA = ду

Q: Show that the line integral | 2.xe- dx + (2y – a²e¬") dy is independent of path and evaluate the…

A: Here we have to show that the given line integral is path independent and evaluate the line integral…

Q: 4. Find the area bounded by the curve (x+y)^5 = ax^2y^2 in the 1st quadrant, where a is a constant.…

A: Let x=rcos2θ, y=rsin2θ L.H.S: x+y5  rcos2θ+rsin2θ5=rcos2θ+sin2θ5                          =r5…

Q: Find the area bounded by the two curves f(x) = x² – 8x + 8 and g(x) = - 2² + 6x – 8, and the two…

A: To find Area between two curves:  f(x)=x2-8x+8 and g(x)=-x2+6x-8 and two vertical lines x=3 and x=4.…

Q: Write an iterated integral of a continuous function fover the region bounded by y =x, y = 2x-4, and…

A:

Q: – 4V5 )ds]

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Q: Find the area bounded by the curve y = x² and y = x+ WRITE THE GIVEN AND DETAILED SOLUTION

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Q: TRUE OR FALSE? The given line integral is independant of path.

A: The given line integral is ∫C2xz3+6ydx+6x-2yzdy+3x2z2-y2dz Compare the above line integral with…