Exercises relating to various topics we have studied.

A key skill to practice is deciding which of the several techniques we have learned should be applied to a particular problem. In these exercises and questions, you will be responsible for choosing a method which works for you.
Compute the indefinite integral. (You should choose an answer which equals at ; if your answer does not satisfy this, add a constant to make it so.)
Integrate by parts.
Let and .
Compute the indefinite integral. (You should choose an answer which equals at ; if your answer does not satisfy this, add a constant to make it so.)
Partial fractions won’t help in this case because the expression is already simplified as much as possible.
Try a trigonometric substitution
Make the substitution .
You should arrive at the integral after the substitution; here you’ll need to use a power-reduction formula to continue.

Sample Quiz Questions

The region in the plane between the -axis and the graph in the range is revolved around the axis . Compute the volume of the resulting solid.

Consider the region given by and . Compute the -coordinate of the centroid (i.e., assuming constant density).

Sample Exam Questions

An object moves in such a way that its acceleration at time seconds is meters per second squared. If the initial velocity of the object is meters per second, what is the limit of its velocity as ?

meters per second meters per second meters per second meters per second meters per second meters per second

Find the volume of the solid generated by revolving the region bounded above by and bounded below by for about the line .

none of these

Evaluate .

none of these