ma104-mid-F08 - MA104 Midterm Test Page 1 of 2 1 Evaluate the following integrals[5 marks(a sin2 x dx cos3 x[5 marks(b tan3(4x dx[5 marks(c cos5 x sin4

# ma104-mid-F08 - MA104 Midterm Test Page 1 of 2 1 Evaluate...

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MA104 — Midterm Test October 23, 2008 Page 1 of 2 1. Evaluate the following integrals.(a)sin2xcos3xdx[5 marks](b)tan3(4x)dx[5 marks](c)cos5xsin4x dx[5 marks]2. By using a suitable trigonometric substitution, evaluate the integral63x2-9x2dx.[8 marks]3. (a) Evaluate the improper integralπ/20sin 2xcosxdxor show that it is divergent.[5 marks](b) Use the Comparison Theorem to determine whether the improper integralπsin2xxdx[5 marks]is convergent or divergent.4. LetRbe the region bounded by the curvesy= 1-x2andy= 4-4x2. Find the volume of[10 marks] 0 5. Find the arc length of the curve defined byy=x-x2+ sin-1(x), 0x1. [ 8 marks ] 6. Find an equation of the curvey=f(x) that satisfies the differential equationdydx=xcosx2y+e3y[9 marks]