Find the area bounded by the curves y= x^2 + 4 and y=x + 2
To find the area bounded by the curves y = x^2 + 4 and y = x + 2, we need to determine the points of intersection of these curves.
Step 1: Set the two equations equal to each other:
x^2 + 4 = x + 2
Step 2: Rearrange the equation to solve for x:
x^2 - x + 2 = 0
Step 3: Solve this quadratic equation by factoring or using the quadratic formula.
Since the quadratic equation does not factor easily, we can use the quadratic formula:
x = (-(-1) ± √((-1)^2 - 4(1)(2))) / (2(1))
Simplifying the equation:
x = (1 ± √(1 - 8)) / 2
x = (1 ± √(-7)) / 2
Since the square root of a negative number is not real, there are no real solutions to the equation x = (1 ± √(-7)) / 2.
Step 4: Since there are no points of intersection, there is no bounded area between the curves y = x^2 + 4 and y = x + 2.