Math 121 - Chapter 5 Study Guide
- Use a simple formula from geometry to find the area function A(x) that gives the area of
the graph of the function on the interval. Look at problems 5.1.9-14.
- Find the derivative and state a corresponding integration formula. Look at problems
- Express the Riemann Sum as a definite integral. Do not evaluate. Look at problems
- Evaluate the indefinite integrals. Three parts. Look at problems 5.2.9-28
- Evaluate the summation. Two parts. Look at problems 5.4.1-2.
- Evaluate the integrals by making appropriate substitutions. Three parts. Look at
- Write the expression in sigma notation, but do not evaluate. Two parts. Look at
- Use the areas shown in the figure to find the definite integrals. Five parts. Look at
- Use part 2 of the fundamental theorem of calculus to evaluate the derivative. Look at
- Express the sum in closed form. Look at problems 5.4.17-20.
- Find a polynomial function with the indicated extrema and y-intercept. Use the fact that
extrema of a polynomial occur when f'(x)=0 to find the derivative function and then
integrate to find the original function f. Use the y-intercept as an initial value.
- Sketch the region whose signed area is represented by the definite integral, and evaluate
the integral using an appropriate formula from geometry. Look at problems 5.5.11-14.
- Find the average value of the function over the given interval. Find all values guaranteed
by the mean value theorem for integrals and then draw a figure that illustrates the mean
value theorem for integrals. Look at problems 5.7.53-54.
- Evaluate the integrals using the first fundamental theorem of calculus. Three parts. Look
at problems 5.6.7-19.
- Evaluate the definite integrals using substitution. Three parts. Look at problems 5.8.3-12.
- A particle moves along an s-axis. Use the given information to find the position function
of the particle. Look at problems 5.7.7-10.
- A particle moves with the given acceleration and initial velocity. Find the displacement
and distance traveled by the particle during the time period. Look at problems 5.7.15-18.
- Some of the problems are directly from the text.