1. Calculate the total area of the region described. Do not count area beneath t
ID: 2850245 • Letter: 1
Question
1. Calculate the total area of the region described. Do not count area beneath the x-axis as negative. HINT [See Example 6.]
Bounded by the curve y = sqrt(x), the x-axis, and the lines x = 0 and x = 25
2. The marginal cost of producing the xth box of light bulbs is 6 + x2/1,000 dollars. Determine how much is added to the total cost by a change in production from x = 10 to x = 100 boxes. HINT [See Example 5.]
3. A ball thrown in the air has a velocity of
v(t) = 99 32t ft/sec at time t seconds. Find the total displacement of the ball between times t = 1 second and t = 6 seconds.
Explanation / Answer
1) y = x , x = 0 , x = 25
Area under curve = [ 0 to 25] x dx
= [ 0 to 25] (x)3/2/(3/2)
= (2/3)(25)3/2
= (2/3)(53)
= 250/3
= 83.33 square units
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