RandolphT4bW98

# RandolphT4bW98 - Winter 1998 Math 21 Test#4b(50 pts Name...

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Winter 1998 Math 21 Test #4b (50 pts) Name Show all your work in answering each question. 1. (8) Solve the diﬀerential equation y 0 + xy =0, y (0)=2. 2. (5) Set up, but do not evaluate , the integral for the length of the curve y = x 3 for 0 x π 2 . b) (3) How is the “arclength function” for this curve deﬁned? s ( x )= 3. (6) Calculate the moment about the x -axis for the region enclosed by the curves y = x and y = x . Assume a uniform density of 1. 4. For this question, consider the curve represented by the parametric equations x = t - 1 y = t 3 - 3 t for 0 t 2 . (a) (3) Sketch this curve. (b) (5) Eliminate the parameter, t , to ﬁnd a corresponding Cartesian equation involving only x and y . 5. Given the parametric equations x = cos
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