Q4. State Green's theorem for the plane. Verify Green's theorem in the plane for O (3x2 – 8y2)dx + (4y – 6xy)dy where C is the region bounded by the parabolas y = x², x = y². Also determine the area...

Choose K=5, please answer all the questions

Extracted text: Q4. State Green's theorem for the plane. Verify Green's theorem in the plane for O (3x2 – 8y2)dx + (4y – 6xy)dy where C is the region bounded by the parabolas y = x², x = y². Also determine the area of the region bounded by the parabolas y = x², x = y². Q5. State Gauss's Divergence theorem. Verify the theorem for the vector function F = 4xi– 2y j+z’k taken over the region bounded by x² + y² = k² and z =0 and z = k .