Calculus and AnalysisEstimate the value of k(0
4 weeks ago
Estimate the value of k(0<k<1) so that the region enclosed by y=1/ sqrt(1-x^(2)) ,y=x, x=0, and x=k has an area of 1 square unit.
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Best Answer
Cecurtis2 Staff answered 4 weeks ago
Set up integral for the area and equate it to 1 int_(0)^(k)[ (1)/(sqrt(1-x^(2)))-x]dx=1 Integrate [ arcsin (x)- (x^(2))/(2)]_(0)^(k)=1 Evaluate and solve using CAS (arcsin (k)- (k^(2))/(2))-(arcsin (0)- (0^(2))/(2))=1 arcsin (k)- (k^(2))/(2)=1 arcsin (k)- (k^(2))/(2)-1=0 k~ 0.9973 Result: k~ 0.9973
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