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Majmaah University College of Engineering Total Marks: 40 Final Exam. Examiner: Dr. Tarek Nabil Ahmed Math. ‘106’ Integral Calculus II Time: 3 hour , 23/2/1434 Answer All Questions Question 1: Evaluate the following integrals: 2 6 2 (1) cos x sin x dx , - (2) x2 2 - x3 dx, (3) 23 4 x dx, 2 (4) x2 5 x6 (5) cosecx dx, dx, (6) sin 3 x cos 7 x dx , (7 ) 4 x2 x 2 2 siny dx, 4 (10) cot xdx, (8) 0 0 e 1 1- x 2 dx , 3 21 (11) 3x 2 z dz dy dx 100 (13) cos(lnx) dx , (14) e 2x 1 - e 4x dx, (9) lnx dx, 1 (12) 1 dx, 1 - cosx (15) x tan -1x dx )20 marks) Question 2: Find the area of the region bounded by the parabola y x yx2 line 2 and the )4 marks) Question 3: Find the volume of the solid generated by revolving the region R bounded by the graphs of the equations x 2 y 2 and 2y - x - 2 0 and the vertical lines x=0 and x=1 about the x-axis. )4 marks) x3 1 Question 4: Find the length of the arc of the curve y from x=1 to x=2 6 2x )4 marks) Question 5: Use the triple integration to find the volume x y z 1, x 0, y 0, z 0 a b c )4 marks) Question 6: Use the double integration to find the area of the region D bounded by x2 1 2 the curves yx , y 2 )4 marks) With my best wishes