Area bounded by curves y=x² -1 and y=1-x² is? A)1/3 B)8/3 C)4/3 D)2/3
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Answer:–
- Area bounded by the curves=8/3
Given:–
The two curves are,
and
Equating both the equations,
Now,
The area between the curves
=
So, The area bounded by the curves is 8/3.
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FORMULA TO BE IMPLEMENTED
The area bounded by the curve y = f(x), the lines x = a, x= b and x axis is given by
EVALUATION
The given curves are
The point of intersection of the above two curves are given by
From Equation (1)
Putting x = 1 we get
Putting x = - 1 we get
Similarly others points are obtained
So all the point of intersections are
The shaded region is bounded by given two curves
Now the region is symmetric about both axis
So the required area is
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