NAME EGN3046: Engineering and Technology Calculus II Exam #02 (Open books and notes. 240 minutes) Solve the following problems within the space provided. The use of programmable calculators and or computers is allowed. Submit your work in a single PDF file via D2L Assignment within the allowed time: 1) Solve the following integral using partial fractions (15 pts.): 3x - x+8 I = ( x 2 + 4 /x - 1) "2) Solve the following integral using Integration by Parts method (15 pts.): I = [x' sin(x)dx3) Find the volume of the solid formed by revolving the region bounded by the curves y = 2 + 2x 3c2 and y = )c2 2x + 2 about the xaXis (15 pts.): 4) Find the center of mass of the plate of uniform thickness (t=]) and uniform density (p:3) bounded by the curves y = 3c2 and y = X3 (15 pts.): 5) Use double integrals to find the volume in the first octane under the plane z =xty and inside the cylinder x2 ty =9. (15 pts.)6) Find the interval of convergence for the following power series. (15 pts.): n=1 2" Vn7) Find the first five terms of the Taylor series expansion of the following function about c =1. (10 pts.): f (x ) = _