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EGET 3171

Review for Exam 3

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1. Determine the volume formed by rotating the area bounded by y = 2 cos x, x=0 and y=0 about the x axis. *(p ^{2})*

2. Find the equation for the curve for which dy/dx = (ln x)

^{2}/x, if the curve passes through the point (1, 6). ( y = (ln(x))^{3}/3 + 6) )

3. A part is to be cut from a piece of 0.25 inch thick sheet. The area of the part can be described as the area under the curve y=e

^{0.2x}between 1 in. and 3 in. The metal weighs 0.30 lb/in^{3}. What will the part weigh when it is completed? (0.225 lb)

4. A particle moves at a velocity described by : v = (sin 4t)/(4+cos4t). Determine an equation for the position of the particle, if the initial position is 0

. (s =1/4 ln(5/(4+cos4t)) )

5. A six foot long board is placed against a wall as shown. Determine the angle q which will maximize the area under the board

. (q =45^{o})

6. Find the area bounded by: y = 0.5e

^{2x}, x = 0, and y = 5. (A=3.51)