# The area of the region bounded by two curves

Please see the attached file.

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

## SOLUTION This solution is **FREE** courtesy of BrainMass!

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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