Let R be the region bounded by the graphs of y=sin(pi x) and y=(x^3)-4x, as shown in the figure above. (a) Find the area of R. (b) The horizontal line y=-2, x=2, x=-1. Write, but do not evaluate, an integral expression for the area.

Without a figure, it is not clear what R stands for.

Here's a plot of the functions. See if it is similar to the figure in your book/exercise. Describe the region R.

The question in part(b) seems incomplete, please check.

Without a figure, it is not clear what R stands for.

Here's a plot of the functions.

http://img862.imageshack.us/i/1299879828.png/

See if it is similar to the figure in your book/exercise. Describe the region R.

The question in part(b) seems incomplete, please check.

go to the calc page... calcmaster/calcAB#3Freeresponse43235. o r g

To find the area of the region R bounded by the two graphs, you need to first determine the points of intersection. The region is bounded by the graphs of y = sin(πx) and y = x^3 - 4x.

Step 1: Set the two equations equal to each other to find the points of intersection.
sin(πx) = x^3 - 4x

Step 2: Set up an integral expression for the area.
Since the line y = -2 is below the curves in question, it acts as the lower boundary for the integral. The horizontal lines x = -1 and x = 2 determine the range of integration.

So, the integral expression for the area is:
∫[from -1 to 2] [upper curve - lower curve] dx

Step 3: Determine the upper and lower curves.
To find the upper and lower curves, set the two equations equal to each other and solve for x. This will give you the x-values at which the two curves intersect.

sin(πx) = x^3 - 4x

Now, you can solve this equation either algebraically or graphically to find the points of intersection.

Step 4: Once you've found the x-values at which the curves intersect, substitute these values back into either equation to find the corresponding y-values.

Step 5: Use the integral expression from step 2 and the coordinates of the points of intersection from step 4 to calculate the area of the region R.

That's it! By following these steps, you can compute the area of the region bounded by the given graphs.