The Riemann integral is usually defined as the limit of a collection of approximating sums. There after, the fundamental theorem of integral calculus provides methods for evaluating integrals without computing limits of sums. Important geometric relationships exist between the graphs of f, the derivative of f and the integral of f. This worksheet compares their graphs and asks the user to identify which is which in an overlay of the three graphs. We present five methods for finding quadratic approximations for the cosine function on this interval.
Techniques use simple differential and integral calculus.
All three questions are addressed in this worksheet . The balance point is located at a point which may be computed as a combination of sums and products of weights and distances from the balance point. For the purposes of the sciences, we often consider a solid as being concentrated at a single point. The location of the center of mass of a continuously distributed weight is computed in this worksheet . This worksheet shows how to calculate the answers and sets Maple up to help do so.