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Applications of the Integral. Areas. Example (1) Find the area A of the region bounded by: y=x 2 + 1, y=x , x=0 & x=1. Example (2) Find the area A of the region bounded by: y=x 2 , y=2x-x 2. Intersections of the Two Curves.

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## Applications of the Integral

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**Example (1)Find the area A of the region bounded by:y=x2 +1,**y=x , x=0 & x=1.**Example (2)Find the area A of the region bounded by:y=x2,**y=2x-x2**Example (3)Find the area A of the region bounded by:y=cosx,**y=sinx, x=0 and x=π/2**Example (4)Find the area A of the region in the first**quadranbounded by:y=x2+ 1 and y-10=0 We second curve’s equation can be rewritten as: y = 10 The curves intersects at the points x=3 and x=-3. We arrive at that by letting x2+ 1=10, which leads to x2=9 The following figures shows the mentioned region. Find the area using two methods!**Example (5)Set up the integral/integrals to find the area A**of the region bounded by:y=9-x2, y=x2 + 1 from x=-4 to x=3

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