Question

Find the total area enclosed by the curves y = |x| and y = x^2-2

Answer 1

Step 1 :

The curve equations are and .

Graph the curves and .

Observe the graph :

The intersection points are (- 2, 2) and (2, 2).

Graphically area of the region obtained by the cyrves is 6.67 sq-units.

Step 2 :

The area between the curves is symmetrical about the y - axis.

So lets find one side and double it.

Thus, area of the region is .

Observe the graph :

Upper curve is .

Lower curve is .

Since We are only using the positive side of , consider .

The boundaries are .

Area of the region enclosed by the given curves is 6.67 sq-units.

Solution:

Area of the region enclosed by the given curves is 6.67 sq-units.