Weekly Assignment 3

Instructions: All integrations must be evaluated by hand. Show your work.

1. Average value

Let f(x)=x(cos(2x)+sin(3x)).

Find the average value of f(x) on [0,π].

Using a graph of f(x), approximate to at least two decimal places all the x-values between 0 and π for which f(x)=average value.

2. Area and Volume

Let R be the region in the plane between one arch of the curve y=cos(x)sin(x) and the x-axis.

Find a range of values of x for this region.

Find the area of R.

Find the volume of the solid of revolution obtained by rotating R about the x axis.