`int_0^(sqrt(3)/2) dr/(sqrt(1 - r^2))` Evaluate the integral

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Textbook Question

Chapter 5, 5.4 - Problem 41 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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

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Therefore the definite integral is equal to

`arcsin(sqrt(3)/2)-arcsin(0)=pi/3-0=pi/3 approx 1.047.`


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