Question 01 a) b) c) d) The figure above shows the ellipse with equation (x 1)² = 16(1 - y²). The ellipse meets the posi

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Question 01 A B C D The Figure Above Shows The Ellipse With Equation X 1 16 1 Y The Ellipse Meets The Posi 1 (205 KiB) Viewed 16 times

Question 01 a) b) c) d) The figure above shows the ellipse with equation (x 1)² = 16(1 - y²). The ellipse meets the positive y and x axes at the points A and B, respectively, as shown in the figure. The elliptic path C is the clockwise selection from A to B. Determine the value of each of the following line integrals. (x-1)²=16(1-y² I. S[(x² + xy)dx + (y² +)dy] S[y³dx + 1/ (x - 1)³ dy] Use Green's theorem to evaluate the line integral fa+ + xy²) dx - x²y dy Where C consists of the arc of the parabola y = x² from (-1,1) to (1,1) Use Stokes' theorem to evaluate ff Curl F.ds Where, F = (z² − 1)i + (z + xy³)j + 6k And S is the portion of x = 6-4y² - 4z² in front of x = -2 with orientation in the negative x-axis direction. Use the Divergence theorem to evaluate fF.ds Where, F = sin(x)i + zy³j+ (z² + 4x)k And S is the surface of the box with -1 ≤ x ≤ 2, 0 ≤ y ≤ 1, and 1 ≤ z ≤ 4. Note that all six sides of the box are included in S. II.