MAC 2312 Midterm: MAC2312 S02 Test 1
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Instructions: write your complete solutions in your exam book. You are not required to simplify your answers. Assume all physical units (length, force, etc. ) are in the kms system, hence are compatible. (1) (40 pts. ) If a force of 50 is required to keep it stretched to a length of 40, how much work is required to stretch it from 30 to 35? (3) (30 pts. ) Let c denote the curve y = (x 2)2, where 1 x 3. In this case, do not evaluate the integrals. (a) the length of c. (b) the area of the surface generated when c is revolved about the (i) x-axis (ii) y-axis (4) (20 pts. ) A tank is shaped like a trapezoidal prism. The bottom is a 10-by-20 rectangle, the top is a 12-by-20 rectangle. Viewed from an end, the tank looks like the trapezoid shown in the gure below.
