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The area of the region bounded by two curves

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Part a. Graph the region bounded by y = 12 - x^2 and y = -x

Part b: Give a formula in terms of x-integral(s) for the area of this region. Do not compute the area.
Part c: Give a formula in terms of y-integral(s) for the area of this region. Do not compute the area.

https://brainmass.com/math/integrals/area-region-bounded-two-curves-178126

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Please see the attached file for graph and formulas

6. Show all of your work on the answer sheet provided. Make sure you read this problem carefully!
Part a: Graph the region bounded by

and

Part b: Give a formula in terms of x-integral(s) for the area of this region. Do not compute the area.
The intersection is at x= -3 and x = 4, therefore, the area is

Part c: Give a formula in terms of y-integral(s) for the area of this region. Do not compute the area.
We separate the total region to two parts A and B.
when , the left-half of the parabola is
The right-half of the parabola is
Then the area of region A is

When , the area of region B is

The total area of the region bounded by the parabola and the line is

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