How do you find the area of the region bounded by the graph of #f(x)=1-x^2# and the #x#-axis on the interval #[-1,1]# ?

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Answer 1 · 2014-09-22T03:28:12

This is a definite integral problem.

#int_-1^1(1-x^2)dx#

#=[x-x^3/3]_-1^1#

#=[(1)-(1)^3/3-((-1)-(-1)^3/3)]#

#=[1-1/3-(-1-(-1)/3)]#

#=[1-1/3-(-1+1/3)]#

#=[1-1/3+1-1/3]#

#=[2-2/3]#

#=[6/3-2/3]#

#=[4/3]=1.3333-># Solution