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

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

asked Mar 7, 2015 in CALCULUS by anonymous

1 Answer

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Step 1 :

The curve equations are image and image.

Graph the curves image and image.

image

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 image.

Observe the graph :

Upper curve is image.

Lower curve is image.

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

The boundaries are image.

image

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.

answered Mar 7, 2015 by lilly Expert

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