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1. Suppose an object is thrown down from a cliff with an initial speed of 7 feet per sec, and its speed in ft/sec after t seconds is given by s(t) = 32t + 7. If the object lands after 5 seconds, how high (in ft) is the cliff? 2. A car is traveling due east. Its velocity (in miles per hour) at time t hours is given by v(t) = −2.5t 2 + 10t + 50. How far did the car travel during the first five hours of the trip? 3. What is the average of f(x) = x 2 over the interval [4,9] ? 4. Suppose the average value of f(x) on the interval [4,7] is 45. Calculate Z 7 4 f(x)dx Suppose a car travels in a straight line at an average velocity of 45 miles per hour. How far does the car travel from 4:00 PM to 7:00 PM ? 5. Evaluate the integral Z T 2 x 2 + 17 x 2 dx 6. Evaluate the integral Z 7 0 2x x 2 + 12 7. Evaluate the integral Z 9 1 (2x)(x 2 + 1)3 dx

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Calculus Problems
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