Exam 8: Integration Techniques

Solve the problem. -The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30-minute period after a thunderstorm. Use the Trapezoidal Rule to estimate the total amount of water flowing into the pond during this period. Round your answer to the nearest gallon.

Give the appropriate form of the partial fraction decomposition. -

Solve the problem by integration. -Find the first-quadrant area bounded by and

Solve the problem. -The voltage v (in volts) induced in a tape head is given by where t is the time (in seconds). Find the average value of v over the interval from t = 0 to t = 4. Round to the nearest volt.

Determine whether the integral converges or diverges. -

Solve the problem. -Find the volume of the solid generated by revolving the region bounded by the curve and the about the x-axis.

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -

Evaluate the integral. -

Evaluate the integral. -

Evaluate the integral. -

Find the area or volume. -Find the area of the region bounded by the curve y = 10 , the x-axis, and on the left by x = 1.

Evaluate the integral by making a substitution and then using a table of integrals. -

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -dx

Evaluate the integral. - dx

Evaluate the improper integral. -

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -

Evaluate the integral. -dx

Use Simpson's Rule with n = 4 steps to estimate the integral. -

Express the integrand as a sum of partial fractions and evaluate the integral. -

Solve the problem. -Estimate the area of the surface generated by revolving the curve y = 2 , 0 $\le$ x $\le$ 3 about the x-axis. Use Simpson's Rule with n = 6.