SOLUTION: Region R is bounded by the curve y = x^2 + 2 and the line y = 6 - x^2 . Find intersection point between two graph and area of R. Sketch the graph.

Question 1130687: Region R is bounded by the curve y = x^2 + 2 and the line y = 6 - x^2 . Find intersection point between two graph and area of R. Sketch the graph.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
y = x^2 + 2 = f(x)
y = 6 - x^2 = g(x)
Adding the two equations, we get 2y = 8 -> y = 4
Solve for x:
4 = x^2 + 2 -> x = +-sqrt(2)
The area bounded by the two curves is given by the integral of the difference
between g(x) and f(x) from -sqrt(2) and sqrt(2).
I will leave that as an exercise for you to determine the integral.

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