Calculus and AnalysisEvaluate the definite integral from 1 to 2 e^(1)/x/x^(2)dx
4 weeks ago
Evaluate the definite integral from 1 to 2 e^(1)/x/x^(2)dx
1 Answers
Best Answer
cindyleonard3 Staff answered 4 weeks ago
int_(1)^(2)(e^(1/x))/(x^(2))dx Substitute (1)/(x)=u And -(dx)/(x^(2))=du Limits of Integration will change from int_(1)^(2) to int_(1/1)^(1/2)=int_(1)^(1/2) =-int_(1)^(2)e^(1/x)(-(dx)/(x^(2))) =-int_(1)^(1/2)e^(u)du Remember that int_(a)^(b)f(x)dx=-int_(b)^(a)f(x)dx -int_(1/2)^(1)e^(u)du=[e^(u)]_(1/2)^(1)=e^(1)-e^(1/2)=e-sqrt(e) Result: int_(1)^(2)(e^(1/x))/(x^(2))dx=e-sqrt(e)
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