`int_(1/2)^(1/sqrt(2))(4/(sqrt(1 - x^2)))dx` Evaluate the integral.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

Hello!

This integral is a table one, `int((4)/(sqrt(1-x^2)))dx=4arcsin(x)+C.`

Therefore the definite integral is equal to

`4*(arcsin(1/sqrt(2))-arcsin(1/2))=4*(pi/4-pi/6)=4*pi/12=pi/3 approx 1.047.`