The area of the region bounded by the given curves.
The area A of the region bounded by the curves y=fx& y=gx and the lines x=a, x=b, where f and g are continuous and fx≥g(x) for all x in a, b, is
The region bounded by curves y=1-2x2 and y=|x|.
As the given region is bounded by curves y=1-2x2 and y=|x|,
From the graph, the region is symmetric about y axis.Therefore, consider x≥0 double the given area.
If x≥0, then x=x, and the graphs intersect when x=1-2x2. That is when
Therefore, either x=12 or x=-1, but -1<0 so x=12
Hence, the limits of integration is from x=0 to x=12
The upper boundary curve is y=1-2x2 and the lower boundary curve is y=x
Therefore, the area of the region bounded by the curves y=1-2x2 and y=|x| is given by
By using fundamental theorem of calculus and power rule,
The area of region bounded by curves y=1-2x2 and y=|x| is A=712 sq.unit