1. What are three different methods for finding the area of a geometric region i

Question

1. What are three different methods for finding the area of a geometric region in the plane?

2.. Can all three methods be used on any region in the plane? Explain.

What are three different methods for finding the area of a geometric region in the plane? Can all three methods be used on any region in the plane? Explain. Explain the differences in evaluating the definite integral for f(x) = 4 - x2 f(x)=4?x2on -1, 3 [?1,3] versus finding the area of the region bounded by the curve f(x) = 4 - x2 f(x)=4?x2 and the x-axis on [-1,3].

Explanation / Answer

you can't use the basic area methods like cutting the graph to square/rectangle/triangle in the irregular shapes

however, you can integrate any shape so far as long as you have bounds. Without bounds it will be hard but not impossible

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