Spring 2006

Show all work in a neat and organized fashion. Clearly indicate your answers.

20 points possible.

1. (4 pts.) The velocity graph of a braking car is shown on a supplemental page. Estimate the distance travelled by the car from time t=0 to time t=8 seconds, by using a right sum with 4 rectangles.

2. (4 pts.) The graph of g consists of two straight lines and a semicircle, shown on a supplemental page. Use the graph to evaluate the integral.

ó õ 10 0  g(x) dx

3. (4 pts.) Find the left Riemann sum for the function f(x)=3+x² over the interval 2 £ x £ 14 using four rectangles of equal width.

4. (4 pts.) Find ò₄⁴ tanx dx.

5. (4 pts.) If ò₁¹¹f(x) dx=6, ò₁₁¹⁵f(x) dx=3, and ò₁⁴f(x) dx=18, find ò₄¹⁵f(x) dx.