FIND THE AREA OF THE REGION BOUNDED BY THE CURVES Y= X^2 + 4X + 3 AND Y= x-1.

There is no area.

The two graphs do not intersect , so you have no closed region.

To find the area of the region bounded by two curves, you need to find the points of intersection between the curves and determine the limits of integration.

First, let's find the points of intersection between the curves y = x^2 + 4x + 3 and y = x - 1:

Set the two equations equal to each other:
x^2 + 4x + 3 = x - 1

Rearrange to bring all terms to one side:
x^2 + 3x + 4 = 0

To solve this quadratic equation, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 1, b = 3, and c = 4.

Applying the quadratic formula, we find:
x = (-3 ± √(3^2 - 4 * 1 * 4)) / (2 * 1)
x = (-3 ± √(9 - 16)) / 2
x = (-3 ± √(-7)) / 2

Since the discriminant (-7) is negative, the equation has no real solutions. Therefore, the two curves do not intersect.

Without any intersection points, the region bounded by the curves does not exist, and the area cannot be calculated.