Question

Sketch the regions enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its heightand width.

y=3sin[(πx)/4] , y= 3x/3

Then find the area S of the regions

Answer 1

The functions are y=3sin[πx/4] and y=x (the 3's cancel out).

We first need to find intersection points. This is done by setting the two equations together:

3sin[πx/4] =x, and using an equation solver (it's necessary),

x₀= 0 and x₁= 2.635

Now we integrate the upper curve and subract the integral of the lower curve. The upper curve in this case (according to the attached graph) is thesin curve:

S === 2.824