Area Under Simple Curves

Step 1: Rearranging both equations into standard parabola form.

• First equation:
• Second equation:

Step 2: Find points of intersection.

Equating both expressions for : Multiply both sides by 24:

So the curves intersect at and

Step 3: Area between vertical curves using horizontal strips.
Use: Here:

Simplify the integrand:

First write both fractions with common denominator:

Bring both terms to same base:

So the integrand is: Since the function is even, use symmetry:

Compute each integral:

Take absolute value, since area cannot be negative: