Solved Problems for Applications

Here we will show typical examples of applications of integrals.

If you wish to simultaneously follow another text on applications in a separate window, click here for Theory and here for Methods Survey.

Problems:

• Problem: Find the average of f (x) = arctan(x) over the interval [−1,2].

• Problem: Find the area of the region

  

• Problem: Find the area of the finite region bounded by the graphs of

  

• Problem: Find the area of a disc of radius R.

• Problem: Find the circumference of a circle of radius R.

• Problem: Consider the finite three-sided region R bounded by the graphs of

  

  Find the volume of the solid obtained by revolving this region about the axis given by y = −1.

• Problem: Consider the region R under the the graph of the function

  

  Find the volume of the solid obtained by revolving this region about the y-axis.

• Problem: Find the surface of a torus (a "tire") with radius of a cross-section equal to r and the radius of rotation of the center of cross-section equal to R.

• Problem: Find the center of gravity of a regular cone whose height is h and the radius of its circular base is r, assuming that it is made of a homogeneous material.

• Problem: Find the value of B(2,1/2).

• Problem: Find the volume of a regular cone whose height is h and the radius of its circular base is r.