Find the area bounded by `y=1/(x^2-2x+2)`
and x-axis.
Text Solution
Verified by Experts
`y=(1)/((x-1)^(2)+1)` When `x=1, ""^(y)"max ."1` When `xrarrpmoo,yrarr0` Therefore, x-axis is the asymptote. Also `f(1+x)=f(1-x)` Hence, the graph is symmetrical about line x = 1 From these information the graph of function is as shown in the figure. `"Area "=2overset(oo)underset(1)int(1)/((x-1)^(2)+1)dx=[2tan^(-1)(x-1)]_(1)^(oo)=pi" sq. units."`
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