Sketch the region whose area is given by the definite integral.?

Question

Scarlett Allison · Accepted Answer

We can immediately discount the options on the right because the graphs are not of the function #y = 2- |x|# but instead of #y = 3 - |x|#.   Since the bounds of integration are from #[-2, 2]#, the answer must be the graph on the bottom left (since the areas on [-2, 0] and [0, 2] are both equal and positive and both must be counted).  As you can see this makes a triangle, so the area is simply given by #(b * h)/2 = (4 * 2)/2 = 4# Hopefully this helps!

Isabella Ackerman · Answer

undefined To sketch the region whose area is given by a definite integral, follow these steps:

1. Identify the function and the limits of integration.
2. Integrate the function with respect to the variable within the given limits.
3. Interpret the result as the area under the curve.
4. Sketch the graph of the function within the specified limits.
5. Shade the region enclosed by the curve and the x-axis between the limits of integration.

If you provide the specific function and limits of integration, I can assist you further with sketching the region.