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1. f(x) dx = 24 and f(x) dx = 20 find f(x) dx

2. Using the Taylor series about x = 0 for sin x, approximate sin(0.4) to four decimal places.

3. Let R be the region in the first quadrant between the graphs of y = e^{–x}, y = sin x, and the y-axis. The volume of the solid that results when R is revolved about the x-axis is

4. Use Euler’s Method, with h = 0.2 to estimate y(3), if = 2y - 4x and y(2) = 6.

5. sec^{4} x dx =

6. Let f(x) = cot x dx; 0 < x < π. If = 1, then f(1) =

7.

8. A force of 250 N is required to stretch a spring 5 m from rest. Using Hooke’s law, F = kx, how much work, in Joules, is required to stretch the spring 7 m from rest?