How to find the region bounded by the curve y = 1 - x^2 and the x axis ?

1 Answer
Jul 23, 2018

Answer:

The area of the region bounded by curve and x-axis is :
#A=4/3=1.33.sq.unit#

Explanation:

Here , curve #y=1-x^2# intersect X-axes then

#y=0=>1-x^2=0=>x=+-1#

Let #A(1,0) and A'(-1,0)# be the two point of intersection of

the given curve and x-axis.

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So, the area of the region bounded by curve and x-axis is :

#color(blue)(A=|I| ,where ,I=int_a^bydx#

#:.I=int_(-1)^1 (1-x^2)dx#

#=2int_0^1 (1-x^2)dx#

#=2[x-x^3/3]_0^1#

#=2[1-1^3/3-0]#

#=2[1-1/3]#

#=2[2/3]#

#=4/3#

Hence,

#A=|4/3|=4/3~~1.33. sq. units#