Find the area between the following curves on the given interval.

Question

Quizplus · Accepted Answer

To find the area between the curves, we must first find the points of intersection. Equating the two curves, we get y = x^2 and y = 4-x^2. Solving for x, we get x = ±sqrt(2). Since the parabola is above the line segment, we only need to integrate the difference between the two curves from -sqrt(2) to sqrt(2).

Thus, the area is given by:
∫(4-x^2 - x^2) dx from -sqrt(2) to sqrt(2)
= ∫(4-2x^2) dx from -sqrt(2) to sqrt(2)
= [4x - (2/3)x^3] from -sqrt(2) to sqrt(2)
= 16/3 - (-16/3) 
= 32/3.

Find the Area Between the Following Curves on the Given