14:05 4911 . 1| 3.00 " @ 120 MAT455_JULAI2021_Final Qu... . . . 19- * - y- Sketch the region of integration for integral z2 dz dy dx . Hence, evaluate -3 the integral using spherical coordinates. (10 marks) QUESTION 5 Use the transformations u = x + y and v = = to evaluate x2 x+y-|dA where R is the region enclosed by the graphs x =1-y, x=-y, x3 =6 and x3 =0. (10 marks) @ HakCiptaUniversitiesologi MARA CONFIDENTIAL CONFIDENTIAL w CS/JUL 2021/MAT455 QUESTION 6 Verify Green's Theorem in the calculation of work done by the force F = (xy) i+(2y2 +x)) where the particle starts at (3,0) traverses the upper semicircle x2 + y? =9, and returns to its starting point along the x-axis. (10 marks) QUESTION 7 Given that F= zi + x ] + yk. Use the Stokes' theorem to evaluate OF . or where C is the boundary of the surface S obtained from the intersection of the plane z= 4 and the cylinder x2 + y2 = 4 above xy-plane, oriented counter clockwise. (10 marks) END OF QUESTION PAPER 3 of 4 O O