1. Let B(x) represent the area bounded by the graph and the horizontal axis and vertical lines at t=0 and t=x for the graph in Fig. 26. Evaluate B(x) for x = 1, 2, 3, 4, and 5.
2.
3. Sketch the function and find the smallest possible value and the largest possible value for a Riemann sum of the given function and partition
4. For f(x) = 3 + x, partition the interval [0, 2] into n equally wide subintervals of length
∆x = 2/n.
(a) Write the lower sum for this function and partition, and calculate the limit of the lower sum as n → ∞.
(b) Write the upper sum for this function and partition and find the limit of the upper sum as n → ∞.
6. Sketch the graph of the integrand function and use it to help evaluate the integral.
9. The velocity of a car after t seconds is feet per second. (a) How far does the car travel during its first 10 seconds? (b) How many seconds does it take the car to travel half the distance in part (a)?
(b) Half of the distance in part (a) is 500 feet. Setting the distance function equal
to 500 and solving for t gives:
10. Find the exact area under half of one arch of the sine curve
